Statistical functions from the Rust statrs crate - 34 aggregates and 509 scalars covering every statrs module
Maintainer(s):
shijianjs
Installing and Loading
INSTALL duckfn_statrs FROM community;
LOAD duckfn_statrs;
Example
-- Summary statistics are aggregates over a DOUBLE column
SELECT sr_mean(x) FROM (VALUES (1.0), (2.0), (3.0)) t(x);
-- 2.0
SELECT g, sr_median(x) FROM (VALUES (1, 3.0), (1, 1.0), (1, NULL), (2, 10.0)) t(g, x) GROUP BY g ORDER BY g;
-- 1 | 2.0
-- 2 | 10.0
-- Distribution functions are scalars, evaluated row by row
SELECT sr_normal_quantile(0.975, 0.0, 1.0);
-- 1.9599639845400538
About duckfn_statrs
Wraps the Rust statrs crate as DuckDB functions - currently 34 aggregates and 509 scalars, covering every statrs module: statistics (means, order statistics incl. percentile / ranks, variance families, covariance of two row-paired columns), distribution (20 continuous and 8 discrete univariate incl. Categorical, 4 multivariate over LIST vectors and row-major flattened matrices, Empirical as aggregates, plus rand-integration sampling for all of them incl. statrs' BinomialAlgorithm sampler), density (kde_pdf / knn_pdf via the kde feature), function (erf / gamma / beta families, factorials, harmonic numbers, logistic / logit, nine kernels selected by name, polynomial evaluation), generate (waveform and log-spaced sequences) and stats_tests (t-test, skewtest, Anderson-Darling, two-sample KS, Mann-Whitney U, chi-square, one-way ANOVA, Fisher's exact - returning [statistic, p-value]). Integer slots (binomial n, pmf x, sample k) are UBIGINT/BIGINT arguments - a non-integer literal does not bind.
Constants follow statrs: the mathematical ones plus its own floating-point precision thresholds with sr_almost_eq, so a query can reuse statrs' notion of "close enough" instead of hard-coding an epsilon.
NULL semantics follow statrs and propagate to the SQL side: a NULL row never enters an aggregate; whatever statrs cannot define (empty group, sample variance of one value, an out-of-range tau, negatives in the geometric / harmonic means) comes back as NULL, never as a NAN value. A parameter that is present but invalid (std_dev <= 0, a probability outside [0, 1], a non-integer where statrs wants one) fails the query.
Requires DuckDB 1.3 or newer: the extension is built against DuckDB 1.5.6 headers but declares the C API floor it needs (v1.2.0), so one binary loads into 1.3.2 through 1.5.6 alike. Development notes and the full function table live in the repository: https://github.com/shijianjs/duckfn-statrs.
Added Functions
| function_name | function_type | description | comment | examples |
|---|---|---|---|---|
| sr_2_sqrt_e_over_pi | scalar | The constant 2*sqrt(e/PI) | NULL | [SELECT sr_2_sqrt_e_over_pi()] |
| sr_abs_max | aggregate | Largest absolute value in a DOUBLE column (statrs' Statistics::abs_max), NULL when no row is non-NULL | NULL | [SELECT sr_abs_max(x) FROM (VALUES (0.0), (3.0), (-8.0)) t(x)] |
| sr_abs_min | aggregate | Smallest absolute value in a DOUBLE column (statrs' Statistics::abs_min), NULL when no row is non-NULL | NULL | [SELECT sr_abs_min(x) FROM (VALUES (3.0), (-2.0)) t(x)] |
| sr_almost_eq | scalar | Whether two DOUBLEs are within the absolute tolerance acc of each other (statrs' almost_eq); infinities only match themselves and NaN never matches | NULL | [SELECT sr_almost_eq(0.1 + 0.2, 0.3, 1e-9)] |
| sr_anderson_darling | scalar | Anderson-Darling goodness-of-fit test of a LIST(DOUBLE) sample against a named distribution (normal / lognormal / exponential / gumbel / weibull / uniform) with its parameter LIST: LIST [A-squared, 5% critical value] | NULL | [SELECT sr_anderson_darling([1.0, 2.0, 3.0, 4.0], 'normal', [2.5, 1.0])] |
| sr_bernoulli_cdf | scalar | Bernoulli cumulative distribution function P(X <= x) | NULL | [SELECT sr_bernoulli_cdf(1, 0.7)] |
| sr_bernoulli_entropy | scalar | Bernoulli entropy | NULL | [SELECT sr_bernoulli_entropy(0.7)] |
| sr_bernoulli_ln_pmf | scalar | Bernoulli log probability mass at x | NULL | [SELECT sr_bernoulli_ln_pmf(1, 0.7)] |
| sr_bernoulli_max | scalar | Bernoulli maximum of the support (1) | NULL | [SELECT sr_bernoulli_max(0.7)] |
| sr_bernoulli_mean | scalar | Bernoulli mean | NULL | [SELECT sr_bernoulli_mean(0.7)] |
| sr_bernoulli_median | scalar | Bernoulli median | NULL | [SELECT sr_bernoulli_median(0.7)] |
| sr_bernoulli_min | scalar | Bernoulli minimum of the support (0) | NULL | [SELECT sr_bernoulli_min(0.7)] |
| sr_bernoulli_mode | scalar | Bernoulli mode | NULL | [SELECT sr_bernoulli_mode(0.7)] |
| sr_bernoulli_pmf | scalar | Bernoulli probability mass P(X = x) for x in {0, 1}, given success probability p | NULL | [SELECT sr_bernoulli_pmf(1, 0.7)] |
| sr_bernoulli_quantile | scalar | Bernoulli quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_bernoulli_quantile(0.5, 0.7)] |
| sr_bernoulli_sf | scalar | Bernoulli survival function P(X > x) | NULL | [SELECT sr_bernoulli_sf(0, 0.7)] |
| sr_bernoulli_skewness | scalar | Bernoulli skewness | NULL | [SELECT sr_bernoulli_skewness(0.7)] |
| sr_bernoulli_std_dev | scalar | Bernoulli standard deviation | NULL | [SELECT sr_bernoulli_std_dev(0.7)] |
| sr_bernoulli_variance | scalar | Bernoulli variance | NULL | [SELECT sr_bernoulli_variance(0.7)] |
| sr_beta | scalar | Beta function B(a, b) | NULL | [SELECT sr_beta(2.0, 3.0)] |
| sr_beta_cdf | scalar | Beta cumulative distribution function P(X <= x) | NULL | [SELECT sr_beta_cdf(0.5, 2.0, 3.0)] |
| sr_beta_entropy | scalar | Beta differential entropy, given shape_a and shape_b | NULL | [SELECT sr_beta_entropy(2.0, 3.0)] |
| sr_beta_incomplete | scalar | Incomplete Beta function B(x; a, b), integrating from 0 to x | NULL | [SELECT sr_beta_incomplete(2.0, 3.0, 0.5)] |
| sr_beta_ln_pdf | scalar | Beta log-density at x | NULL | [SELECT sr_beta_ln_pdf(0.5, 2.0, 3.0)] |
| sr_beta_max | scalar | Beta maximum of the support (1) | NULL | [SELECT sr_beta_max(2.0, 3.0)] |
| sr_beta_mean | scalar | Beta mean, given shape_a and shape_b | NULL | [SELECT sr_beta_mean(2.0, 3.0)] |
| sr_beta_min | scalar | Beta minimum of the support (0) | NULL | [SELECT sr_beta_min(2.0, 3.0)] |
| sr_beta_mode | scalar | Beta mode, given shape_a and shape_b | NULL | [SELECT sr_beta_mode(2.0, 3.0)] |
| sr_beta_pdf | scalar | Beta probability density at x, given shape_a and shape_b | NULL | [SELECT sr_beta_pdf(0.5, 2.0, 3.0)] |
| sr_beta_quantile | scalar | Beta quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_beta_quantile(0.5, 2.0, 3.0)] |
| sr_beta_regularized | scalar | Regularized incomplete Beta function I(x; a, b) | NULL | [SELECT sr_beta_regularized(2.0, 3.0, 0.5)] |
| sr_beta_sf | scalar | Beta survival function P(X > x) | NULL | [SELECT sr_beta_sf(0.5, 2.0, 3.0)] |
| sr_beta_skewness | scalar | Beta skewness, given shape_a and shape_b | NULL | [SELECT sr_beta_skewness(2.0, 3.0)] |
| sr_beta_std_dev | scalar | Beta standard deviation, given shape_a and shape_b | NULL | [SELECT sr_beta_std_dev(2.0, 3.0)] |
| sr_beta_variance | scalar | Beta variance, given shape_a and shape_b | NULL | [SELECT sr_beta_variance(2.0, 3.0)] |
| sr_binomial_cdf | scalar | Binomial cumulative distribution function P(X <= x) | NULL | [SELECT sr_binomial_cdf(3, 0.5, 10)] |
| sr_binomial_entropy | scalar | Binomial entropy | NULL | [SELECT sr_binomial_entropy(0.5, 10)] |
| sr_binomial_ln_pmf | scalar | Binomial log probability mass at x | NULL | [SELECT sr_binomial_ln_pmf(3, 0.5, 10)] |
| sr_binomial_max | scalar | Binomial maximum of the support (n) | NULL | [SELECT sr_binomial_max(0.5, 10)] |
| sr_binomial_mean | scalar | Binomial mean | NULL | [SELECT sr_binomial_mean(0.5, 10)] |
| sr_binomial_median | scalar | Binomial median | NULL | [SELECT sr_binomial_median(0.5, 10)] |
| sr_binomial_min | scalar | Binomial minimum of the support (0) | NULL | [SELECT sr_binomial_min(0.5, 10)] |
| sr_binomial_mode | scalar | Binomial mode | NULL | [SELECT sr_binomial_mode(0.5, 10)] |
| sr_binomial_pmf | scalar | Binomial probability mass P(X = x), given success probability p and number of trials n | NULL | [SELECT sr_binomial_pmf(3, 0.5, 10)] |
| sr_binomial_quantile | scalar | Binomial quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_binomial_quantile(0.5, 0.5, 10)] |
| sr_binomial_sf | scalar | Binomial survival function P(X > x) | NULL | [SELECT sr_binomial_sf(3, 0.5, 10)] |
| sr_binomial_skewness | scalar | Binomial skewness | NULL | [SELECT sr_binomial_skewness(0.5, 10)] |
| sr_binomial_std_dev | scalar | Binomial standard deviation | NULL | [SELECT sr_binomial_std_dev(0.5, 10)] |
| sr_binomial_variance | scalar | Binomial variance | NULL | [SELECT sr_binomial_variance(0.5, 10)] |
| sr_categorical_cdf | scalar | Categorical cumulative distribution function P(X <= x) | NULL | [SELECT sr_categorical_cdf(1, [1.0, 2.0, 1.0])] |
| sr_categorical_entropy | scalar | Categorical entropy | NULL | [SELECT sr_categorical_entropy([1.0, 2.0, 1.0])] |
| sr_categorical_ln_pmf | scalar | Categorical log probability mass at x | NULL | [SELECT sr_categorical_ln_pmf(1, [1.0, 2.0, 1.0])] |
| sr_categorical_max | scalar | Categorical maximum of the support (last category index) | NULL | [SELECT sr_categorical_max([1.0, 2.0, 1.0])] |
| sr_categorical_mean | scalar | Categorical mean | NULL | [SELECT sr_categorical_mean([1.0, 2.0, 1.0])] |
| sr_categorical_median | scalar | Categorical median | NULL | [SELECT sr_categorical_median([1.0, 2.0, 1.0])] |
| sr_categorical_min | scalar | Categorical minimum of the support (category index 0) | NULL | [SELECT sr_categorical_min([1.0, 2.0, 1.0])] |
| sr_categorical_pmf | scalar | Categorical probability mass P(X = x) for a distribution given by an unnormalised probability LIST (normalised by statrs) | NULL | [SELECT sr_categorical_pmf(1, [1.0, 2.0, 1.0])] |
| sr_categorical_quantile | scalar | Categorical quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_categorical_quantile(0.5, [1.0, 2.0, 1.0])] |
| sr_categorical_sf | scalar | Categorical survival function P(X > x) | NULL | [SELECT sr_categorical_sf(1, [1.0, 2.0, 1.0])] |
| sr_categorical_skewness | scalar | Categorical skewness | NULL | [SELECT sr_categorical_skewness([1.0, 2.0, 1.0])] |
| sr_categorical_std_dev | scalar | Categorical standard deviation | NULL | [SELECT sr_categorical_std_dev([1.0, 2.0, 1.0])] |
| sr_categorical_variance | scalar | Categorical variance | NULL | [SELECT sr_categorical_variance([1.0, 2.0, 1.0])] |
| sr_cauchy_cdf | scalar | Cauchy cumulative distribution function P(X <= x) | NULL | [SELECT sr_cauchy_cdf(1.0, 0.0, 1.0)] |
| sr_cauchy_entropy | scalar | Cauchy distribution differential entropy | NULL | [SELECT sr_cauchy_entropy(0.0, 1.0)] |
| sr_cauchy_ln_pdf | scalar | Cauchy log-density at x | NULL | [SELECT sr_cauchy_ln_pdf(1.0, 0.0, 1.0)] |
| sr_cauchy_max | scalar | Cauchy distribution support maximum (positive infinity) | NULL | [SELECT sr_cauchy_max(0.0, 1.0)] |
| sr_cauchy_mean | scalar | Cauchy distribution mean (undefined) | NULL | [SELECT sr_cauchy_mean(0.0, 1.0)] |
| sr_cauchy_median | scalar | Cauchy distribution median | NULL | [SELECT sr_cauchy_median(0.0, 1.0)] |
| sr_cauchy_min | scalar | Cauchy distribution support minimum (negative infinity) | NULL | [SELECT sr_cauchy_min(0.0, 1.0)] |
| sr_cauchy_mode | scalar | Cauchy distribution mode | NULL | [SELECT sr_cauchy_mode(0.0, 1.0)] |
| sr_cauchy_pdf | scalar | Cauchy probability density at x, given location and scale | NULL | [SELECT sr_cauchy_pdf(1.0, 0.0, 1.0)] |
| sr_cauchy_quantile | scalar | Cauchy quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_cauchy_quantile(0.5, 0.0, 1.0)] |
| sr_cauchy_sf | scalar | Cauchy survival function P(X > x) | NULL | [SELECT sr_cauchy_sf(1.0, 0.0, 1.0)] |
| sr_cauchy_skewness | scalar | Cauchy distribution skewness (undefined) | NULL | [SELECT sr_cauchy_skewness(0.0, 1.0)] |
| sr_cauchy_std_dev | scalar | Cauchy distribution standard deviation (undefined) | NULL | [SELECT sr_cauchy_std_dev(0.0, 1.0)] |
| sr_cauchy_variance | scalar | Cauchy distribution variance (undefined) | NULL | [SELECT sr_cauchy_variance(0.0, 1.0)] |
| sr_chi_cdf | scalar | Chi distribution cumulative distribution function P(X <= x) | NULL | [SELECT sr_chi_cdf(1.0, 2)] |
| sr_chi_entropy | scalar | Chi distribution differential entropy, given UBIGINT freedom | NULL | [SELECT sr_chi_entropy(2)] |
| sr_chi_ln_pdf | scalar | Chi distribution log-density at x | NULL | [SELECT sr_chi_ln_pdf(1.0, 2)] |
| sr_chi_max | scalar | Chi distribution maximum of the support (positive infinity) | NULL | [SELECT sr_chi_max(2)] |
| sr_chi_mean | scalar | Chi distribution mean, given UBIGINT freedom | NULL | [SELECT sr_chi_mean(2)] |
| sr_chi_min | scalar | Chi distribution minimum of the support (0) | NULL | [SELECT sr_chi_min(2)] |
| sr_chi_mode | scalar | Chi distribution mode, given UBIGINT freedom | NULL | [SELECT sr_chi_mode(2)] |
| sr_chi_pdf | scalar | Chi distribution probability density at x (the sqrt-chi-squared distribution), UBIGINT freedom | NULL | [SELECT sr_chi_pdf(1.0, 2)] |
| sr_chi_quantile | scalar | Chi distribution quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_chi_quantile(0.5, 2)] |
| sr_chi_sf | scalar | Chi distribution survival function P(X > x) | NULL | [SELECT sr_chi_sf(1.0, 2)] |
| sr_chi_skewness | scalar | Chi distribution skewness, given UBIGINT freedom | NULL | [SELECT sr_chi_skewness(2)] |
| sr_chi_squared_cdf | scalar | Chi-squared cumulative distribution function P(X <= x) | NULL | [SELECT sr_chi_squared_cdf(1.0, 2.0)] |
| sr_chi_squared_entropy | scalar | Chi-squared differential entropy, given degrees of freedom | NULL | [SELECT sr_chi_squared_entropy(2.0)] |
| sr_chi_squared_ln_pdf | scalar | Chi-squared log-density at x | NULL | [SELECT sr_chi_squared_ln_pdf(1.0, 2.0)] |
| sr_chi_squared_max | scalar | Chi-squared maximum of the support (positive infinity) | NULL | [SELECT sr_chi_squared_max(2.0)] |
| sr_chi_squared_mean | scalar | Chi-squared mean, given degrees of freedom | NULL | [SELECT sr_chi_squared_mean(2.0)] |
| sr_chi_squared_median | scalar | Chi-squared median, given degrees of freedom | NULL | [SELECT sr_chi_squared_median(2.0)] |
| sr_chi_squared_min | scalar | Chi-squared minimum of the support (0) | NULL | [SELECT sr_chi_squared_min(2.0)] |
| sr_chi_squared_mode | scalar | Chi-squared mode, given degrees of freedom | NULL | [SELECT sr_chi_squared_mode(2.0)] |
| sr_chi_squared_pdf | scalar | Chi-squared probability density at x, given degrees of freedom | NULL | [SELECT sr_chi_squared_pdf(1.0, 2.0)] |
| sr_chi_squared_quantile | scalar | Chi-squared quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_chi_squared_quantile(0.95, 2.0)] |
| sr_chi_squared_sf | scalar | Chi-squared survival function P(X > x) | NULL | [SELECT sr_chi_squared_sf(1.0, 2.0)] |
| sr_chi_squared_skewness | scalar | Chi-squared skewness, given degrees of freedom | NULL | [SELECT sr_chi_squared_skewness(2.0)] |
| sr_chi_squared_std_dev | scalar | Chi-squared standard deviation, given degrees of freedom | NULL | [SELECT sr_chi_squared_std_dev(2.0)] |
| sr_chi_squared_variance | scalar | Chi-squared variance, given degrees of freedom | NULL | [SELECT sr_chi_squared_variance(2.0)] |
| sr_chi_std_dev | scalar | Chi distribution standard deviation, given UBIGINT freedom | NULL | [SELECT sr_chi_std_dev(2)] |
| sr_chi_variance | scalar | Chi distribution variance, given UBIGINT freedom | NULL | [SELECT sr_chi_variance(2)] |
| sr_chisquare | scalar | Chi-square goodness-of-fit test on an observed-count LIST(UBIGINT) (expected frequencies optional, defaults to uniform; ddof optional UBIGINT): LIST [chi-square statistic, p-value] | NULL | [SELECT sr_chisquare([16, 18, 16, 14, 12, 12], NULL, NULL)] |
| sr_choose | scalar | Binomial coefficient C(n, k) (statrs' factorial::binomial), n and k UBIGINTs | NULL | [SELECT sr_choose(10, 3)] |
| sr_covariance | aggregate | Sample covariance of two DOUBLE columns (Bessel-corrected), NULL when fewer than two rows are fully non-NULL | A row with a NULL in either column is skipped entirely, keeping the two columns paired | [SELECT sr_covariance(x, y) FROM (VALUES (0.0, -5.0), (3.0, 4.0), (-2.0, 10.0)) t(x, y)] |
| sr_default_eps | scalar | statrs' default target absolute accuracy for f64 operations, 1e-9 | NULL | [SELECT sr_default_eps()] |
| sr_default_f64_acc | scalar | statrs' default absolute comparison tolerance for f64 (0.01 * F64_PREC) | NULL | [SELECT sr_default_f64_acc()] |
| sr_default_relative_acc | scalar | statrs' default target relative accuracy for f64 operations, 1e-14 | NULL | [SELECT sr_default_relative_acc()] |
| sr_default_ulps | scalar | statrs' default target ULPs accuracy for f64 operations (5), as a UINTEGER | NULL | [SELECT sr_default_ulps()] |
| sr_digamma | scalar | Digamma function ψ(x), the derivative of ln(Γ(x)) | NULL | [SELECT sr_digamma(2.0)] |
| sr_dirac_cdf | scalar | Dirac delta cumulative distribution function P(X <= x) | NULL | [SELECT sr_dirac_cdf(1.0, 1.0)] |
| sr_dirac_entropy | scalar | Dirac delta distribution differential entropy | NULL | [SELECT sr_dirac_entropy(1.0)] |
| sr_dirac_max | scalar | Dirac delta distribution support maximum (v) | NULL | [SELECT sr_dirac_max(1.0)] |
| sr_dirac_mean | scalar | Dirac delta distribution mean (always v) | NULL | [SELECT sr_dirac_mean(1.0)] |
| sr_dirac_median | scalar | Dirac delta distribution median (always v) | NULL | [SELECT sr_dirac_median(1.0)] |
| sr_dirac_min | scalar | Dirac delta distribution support minimum (v) | NULL | [SELECT sr_dirac_min(1.0)] |
| sr_dirac_mode | scalar | Dirac delta distribution mode (always v) | NULL | [SELECT sr_dirac_mode(1.0)] |
| sr_dirac_quantile | scalar | Dirac delta quantile function: always the location v | NULL | [SELECT sr_dirac_quantile(0.5, 1.0)] |
| sr_dirac_sf | scalar | Dirac delta survival function P(X > x) | NULL | [SELECT sr_dirac_sf(0.5, 1.0)] |
| sr_dirac_skewness | scalar | Dirac delta distribution skewness (always 0) | NULL | [SELECT sr_dirac_skewness(1.0)] |
| sr_dirac_std_dev | scalar | Dirac delta distribution standard deviation (always 0) | NULL | [SELECT sr_dirac_std_dev(1.0)] |
| sr_dirac_variance | scalar | Dirac delta distribution variance (always 0) | NULL | [SELECT sr_dirac_variance(1.0)] |
| sr_dirichlet_entropy | scalar | Differential entropy of the Dirichlet distribution with concentrations alpha | NULL | [SELECT sr_dirichlet_entropy([1.0, 1.0])] |
| sr_dirichlet_ln_pdf | scalar | Log probability density of x on the simplex, given the concentration vector alpha; x must lie in (0,1)^k and sum to 1 | NULL | [SELECT sr_dirichlet_ln_pdf([0.1, 0.2, 0.3, 0.4], [0.1, 0.3, 0.5, 0.8])] |
| sr_dirichlet_mean | scalar | Mean vector of the Dirichlet distribution (alpha_i / alpha_0) given the concentration vector alpha | NULL | [SELECT sr_dirichlet_mean([1.0, 2.0, 3.0, 4.0])] |
| sr_dirichlet_pdf | scalar | Dirichlet probability density of x on the simplex, given the concentration vector alpha | NULL | [SELECT sr_dirichlet_pdf([0.5, 0.5], [1.0, 1.0])] |
| sr_dirichlet_variance | scalar | Covariance matrix of the Dirichlet distribution (row-major flattened LIST) given the concentration vector alpha | NULL | [SELECT sr_dirichlet_variance([1.0, 2.0])] |
| sr_discrete_uniform_cdf | scalar | Discrete uniform cumulative distribution function P(X <= x) | NULL | [SELECT sr_discrete_uniform_cdf(3, 1, 6)] |
| sr_discrete_uniform_entropy | scalar | Discrete uniform entropy | NULL | [SELECT sr_discrete_uniform_entropy(1, 6)] |
| sr_discrete_uniform_ln_pmf | scalar | Discrete uniform log probability mass at x | NULL | [SELECT sr_discrete_uniform_ln_pmf(2, 1, 6)] |
| sr_discrete_uniform_max | scalar | Discrete uniform maximum of the support (max) | NULL | [SELECT sr_discrete_uniform_max(1, 6)] |
| sr_discrete_uniform_mean | scalar | Discrete uniform mean | NULL | [SELECT sr_discrete_uniform_mean(1, 6)] |
| sr_discrete_uniform_median | scalar | Discrete uniform median | NULL | [SELECT sr_discrete_uniform_median(1, 6)] |
| sr_discrete_uniform_min | scalar | Discrete uniform minimum of the support (min) | NULL | [SELECT sr_discrete_uniform_min(1, 6)] |
| sr_discrete_uniform_mode | scalar | Discrete uniform mode | NULL | [SELECT sr_discrete_uniform_mode(1, 6)] |
| sr_discrete_uniform_pmf | scalar | Discrete uniform probability mass P(X = x) on the integer range [min, max] | NULL | [SELECT sr_discrete_uniform_pmf(2, 1, 6)] |
| sr_discrete_uniform_quantile | scalar | Discrete uniform quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_discrete_uniform_quantile(0.5, 1, 6)] |
| sr_discrete_uniform_sf | scalar | Discrete uniform survival function P(X > x) | NULL | [SELECT sr_discrete_uniform_sf(3, 1, 6)] |
| sr_discrete_uniform_skewness | scalar | Discrete uniform skewness | NULL | [SELECT sr_discrete_uniform_skewness(1, 6)] |
| sr_discrete_uniform_std_dev | scalar | Discrete uniform standard deviation | NULL | [SELECT sr_discrete_uniform_std_dev(1, 6)] |
| sr_discrete_uniform_variance | scalar | Discrete uniform variance | NULL | [SELECT sr_discrete_uniform_variance(1, 6)] |
| sr_empirical_cdf | aggregate | Empirical CDF of a DOUBLE column evaluated at the second (constant) argument | The sample is the whole column; an empty group yields NULL | [SELECT sr_empirical_cdf(v, 2.0) FROM (VALUES (1.0), (2.0), (3.0), (4.0)) t(v)] |
| sr_empirical_entropy | aggregate | Empirical entropy of a DOUBLE column; always NULL, since statrs implements no entropy for the empirical distribution | statrs' Distribution default returns None here, so the result is always NULL | [SELECT sr_empirical_entropy(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_empirical_max | aggregate | Empirical maximum of a DOUBLE column | The sample is the whole column; an empty group yields NULL | [SELECT sr_empirical_max(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_empirical_mean | aggregate | Empirical mean of a DOUBLE column | The sample is the whole column; an empty group yields NULL | [SELECT sr_empirical_mean(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_empirical_min | aggregate | Empirical minimum of a DOUBLE column | The sample is the whole column; an empty group yields NULL | [SELECT sr_empirical_min(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_empirical_quantile | aggregate | Empirical quantile function of a DOUBLE column at the second (constant) probability in [0, 1] | NULL | [SELECT sr_empirical_quantile(v, 0.5) FROM (VALUES (1.0), (2.0), (3.0), (4.0)) t(v)] |
| sr_empirical_sf | aggregate | Empirical survival function of a DOUBLE column evaluated at the second (constant) argument | NULL | [SELECT sr_empirical_sf(v, 2.0) FROM (VALUES (1.0), (2.0), (3.0), (4.0)) t(v)] |
| sr_empirical_skewness | aggregate | Empirical skewness of a DOUBLE column; always NULL, since statrs implements no skewness for the empirical distribution | statrs' Distribution default returns None here, so the result is always NULL | [SELECT sr_empirical_skewness(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_empirical_std_dev | aggregate | Empirical standard deviation of a DOUBLE column | The sample is the whole column; an empty group yields NULL | [SELECT sr_empirical_std_dev(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_empirical_variance | aggregate | Empirical variance of a DOUBLE column | The sample is the whole column; an empty group yields NULL | [SELECT sr_empirical_variance(v) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_erf | scalar | Error function erf(x) | NULL | [SELECT sr_erf(1.0)] |
| sr_erf_inv | scalar | Inverse error function, erf(x) = y solved for x | NULL | [SELECT sr_erf_inv(0.8427007929497149)] |
| sr_erfc | scalar | Complementary error function erfc(x) = 1 - erf(x) | NULL | [SELECT sr_erfc(1.0)] |
| sr_erfc_inv | scalar | Inverse complementary error function, erfc(x) = y solved for x | NULL | [SELECT sr_erfc_inv(0.15729920705028513)] |
| sr_erlang_cdf | scalar | Erlang cumulative distribution function P(X <= x) | NULL | [SELECT sr_erlang_cdf(1.0, 2, 2.0)] |
| sr_erlang_entropy | scalar | Erlang differential entropy (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_entropy(2, 1.0)] |
| sr_erlang_ln_pdf | scalar | Erlang log-density at x | NULL | [SELECT sr_erlang_ln_pdf(1.0, 2, 2.0)] |
| sr_erlang_max | scalar | Erlang maximum of the support (positive infinity) | NULL | [SELECT sr_erlang_max(2, 1.0)] |
| sr_erlang_mean | scalar | Erlang mean (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_mean(2, 1.0)] |
| sr_erlang_min | scalar | Erlang minimum of the support (0) | NULL | [SELECT sr_erlang_min(2, 1.0)] |
| sr_erlang_mode | scalar | Erlang mode (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_mode(2, 1.0)] |
| sr_erlang_pdf | scalar | Erlang probability density at x (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_pdf(1.0, 2, 2.0)] |
| sr_erlang_quantile | scalar | Erlang quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_erlang_quantile(0.5, 2, 2.0)] |
| sr_erlang_sf | scalar | Erlang survival function P(X > x) | NULL | [SELECT sr_erlang_sf(1.0, 2, 2.0)] |
| sr_erlang_skewness | scalar | Erlang skewness (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_skewness(2, 1.0)] |
| sr_erlang_std_dev | scalar | Erlang standard deviation (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_std_dev(2, 1.0)] |
| sr_erlang_variance | scalar | Erlang variance (UBIGINT shape, DOUBLE rate) | NULL | [SELECT sr_erlang_variance(2, 1.0)] |
| sr_euler_mascheroni | scalar | The Euler-Mascheroni constant | NULL | [SELECT sr_euler_mascheroni()] |
| sr_exp_cdf | scalar | Exponential cumulative distribution function P(X <= x) | NULL | [SELECT sr_exp_cdf(1.0, 2.0)] |
| sr_exp_entropy | scalar | Exponential differential entropy, given the rate | NULL | [SELECT sr_exp_entropy(2.0)] |
| sr_exp_ln_pdf | scalar | Exponential log-density at x | NULL | [SELECT sr_exp_ln_pdf(1.0, 2.0)] |
| sr_exp_max | scalar | Exponential maximum of the support (positive infinity) | NULL | [SELECT sr_exp_max(2.0)] |
| sr_exp_mean | scalar | Exponential mean, given the rate | NULL | [SELECT sr_exp_mean(2.0)] |
| sr_exp_median | scalar | Exponential median, given the rate | NULL | [SELECT sr_exp_median(2.0)] |
| sr_exp_min | scalar | Exponential minimum of the support (0) | NULL | [SELECT sr_exp_min(2.0)] |
| sr_exp_mode | scalar | Exponential mode, given the rate | NULL | [SELECT sr_exp_mode(2.0)] |
| sr_exp_pdf | scalar | Exponential probability density at x, given the rate | NULL | [SELECT sr_exp_pdf(1.0, 2.0)] |
| sr_exp_quantile | scalar | Exponential quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_exp_quantile(0.5, 2.0)] |
| sr_exp_sf | scalar | Exponential survival function P(X > x) | NULL | [SELECT sr_exp_sf(1.0, 2.0)] |
| sr_exp_skewness | scalar | Exponential skewness, given the rate | NULL | [SELECT sr_exp_skewness(2.0)] |
| sr_exp_std_dev | scalar | Exponential standard deviation, given the rate | NULL | [SELECT sr_exp_std_dev(2.0)] |
| sr_exp_variance | scalar | Exponential variance, given the rate | NULL | [SELECT sr_exp_variance(2.0)] |
| sr_exponential_integral | scalar | Exponential integral E_n(x) for n (UBIGINT) >= 0 and x >= 0; NULL where statrs leaves it undefined | NULL | [SELECT sr_exponential_integral(1.0, 0)] |
| sr_f64_prec | scalar | F64_PREC: the maximum relative precision 2^-53 of an IEEE 754 double | NULL | [SELECT sr_f64_prec()] |
| sr_f_oneway | scalar | One-way ANOVA over a LIST of sample LISTs: LIST [F statistic, p-value]; NaN policy codes as elsewhere | NULL | [SELECT sr_f_oneway([[1.0, 2.0, 3.0], [3.0, 4.0, 5.0]], 1.0)] |
| sr_factorial | scalar | Factorial of n, n as a UBIGINT (statrs' factorial::factorial) | NULL | [SELECT sr_factorial(10)] |
| sr_fisher_snedecor_cdf | scalar | Fisher-Snedecor (F) cumulative distribution function P(X <= x) | NULL | [SELECT sr_fisher_snedecor_cdf(1.0, 2.0, 3.0)] |
| sr_fisher_snedecor_entropy | scalar | Fisher-Snedecor (F) differential entropy, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_entropy(3.0, 5.0)] |
| sr_fisher_snedecor_ln_pdf | scalar | Fisher-Snedecor (F) log-density at x | NULL | [SELECT sr_fisher_snedecor_ln_pdf(1.0, 2.0, 3.0)] |
| sr_fisher_snedecor_max | scalar | Fisher-Snedecor (F) maximum of the support (positive infinity) | NULL | [SELECT sr_fisher_snedecor_max(3.0, 5.0)] |
| sr_fisher_snedecor_mean | scalar | Fisher-Snedecor (F) mean, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_mean(3.0, 5.0)] |
| sr_fisher_snedecor_min | scalar | Fisher-Snedecor (F) minimum of the support (0) | NULL | [SELECT sr_fisher_snedecor_min(3.0, 5.0)] |
| sr_fisher_snedecor_mode | scalar | Fisher-Snedecor (F) mode, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_mode(3.0, 5.0)] |
| sr_fisher_snedecor_pdf | scalar | Fisher-Snedecor (F) probability density at x, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_pdf(1.0, 2.0, 3.0)] |
| sr_fisher_snedecor_quantile | scalar | Fisher-Snedecor (F) quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_fisher_snedecor_quantile(0.95, 2.0, 3.0)] |
| sr_fisher_snedecor_sf | scalar | Fisher-Snedecor (F) survival function P(X > x) | NULL | [SELECT sr_fisher_snedecor_sf(1.0, 2.0, 3.0)] |
| sr_fisher_snedecor_skewness | scalar | Fisher-Snedecor (F) skewness, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_skewness(3.0, 7.0)] |
| sr_fisher_snedecor_std_dev | scalar | Fisher-Snedecor (F) standard deviation, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_std_dev(3.0, 5.0)] |
| sr_fisher_snedecor_variance | scalar | Fisher-Snedecor (F) variance, given the two degrees of freedom | NULL | [SELECT sr_fisher_snedecor_variance(3.0, 5.0)] |
| sr_fishers_exact | scalar | Fisher's exact test p-value on a 2x2 contingency table given as a 4-entry UBIGINT LIST, row-major; alternative codes as elsewhere | NULL | [SELECT sr_fishers_exact([1, 2, 3, 4], 1.0)] |
| sr_fishers_exact_with_odds_ratio | scalar | Fisher's exact test on a 2x2 contingency table (4-entry UBIGINT LIST, row-major): LIST [odds ratio, p-value] | NULL | [SELECT sr_fishers_exact_with_odds_ratio([1, 2, 3, 4], 1.0)] |
| sr_gamma | scalar | Gamma function Γ(x) | NULL | [SELECT sr_gamma(5.0)] |
| sr_gamma_cdf | scalar | Gamma cumulative distribution function P(X <= x) | NULL | [SELECT sr_gamma_cdf(1.0, 2.0, 2.0)] |
| sr_gamma_entropy | scalar | Gamma differential entropy (shape/rate parameterization) | NULL | [SELECT sr_gamma_entropy(2.0, 1.0)] |
| sr_gamma_ln_pdf | scalar | Gamma log-density at x | NULL | [SELECT sr_gamma_ln_pdf(1.0, 2.0, 2.0)] |
| sr_gamma_lower_incomplete | scalar | Lower incomplete Gamma function γ(a, x), integrating from 0 to x | NULL | [SELECT sr_gamma_lower_incomplete(2.0, 1.0)] |
| sr_gamma_lower_regularized | scalar | Regularized lower incomplete Gamma function P(a, x) = γ(a,x)/Γ(a) | NULL | [SELECT sr_gamma_lower_regularized(2.0, 1.0)] |
| sr_gamma_max | scalar | Gamma maximum of the support (positive infinity) | NULL | [SELECT sr_gamma_max(2.0, 1.0)] |
| sr_gamma_mean | scalar | Gamma mean (shape/rate parameterization) | NULL | [SELECT sr_gamma_mean(2.0, 1.0)] |
| sr_gamma_min | scalar | Gamma minimum of the support (0) | NULL | [SELECT sr_gamma_min(2.0, 1.0)] |
| sr_gamma_mode | scalar | Gamma mode (shape/rate parameterization) | NULL | [SELECT sr_gamma_mode(2.0, 1.0)] |
| sr_gamma_pdf | scalar | Gamma probability density at x (shape/rate parameterization) | NULL | [SELECT sr_gamma_pdf(1.0, 2.0, 2.0)] |
| sr_gamma_quantile | scalar | Gamma quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_gamma_quantile(0.5, 2.0, 2.0)] |
| sr_gamma_sf | scalar | Gamma survival function P(X > x) | NULL | [SELECT sr_gamma_sf(1.0, 2.0, 2.0)] |
| sr_gamma_skewness | scalar | Gamma skewness (shape/rate parameterization) | NULL | [SELECT sr_gamma_skewness(2.0, 1.0)] |
| sr_gamma_std_dev | scalar | Gamma standard deviation (shape/rate parameterization) | NULL | [SELECT sr_gamma_std_dev(2.0, 1.0)] |
| sr_gamma_upper_incomplete | scalar | Upper incomplete Gamma function Γ(a, x), integrating from x to infinity | NULL | [SELECT sr_gamma_upper_incomplete(2.0, 1.0)] |
| sr_gamma_upper_regularized | scalar | Regularized upper incomplete Gamma function Q(a, x) = Γ(a,x)/Γ(a) | NULL | [SELECT sr_gamma_upper_regularized(2.0, 1.0)] |
| sr_gamma_variance | scalar | Gamma variance (shape/rate parameterization) | NULL | [SELECT sr_gamma_variance(2.0, 1.0)] |
| sr_gen_log_spaced | scalar | Log-spaced sequence of length points between 10^start_exp and 10^stop_exp, returned as LIST(DOUBLE) | NULL | [SELECT sr_gen_log_spaced(5, 0.0, 2.0)] |
| sr_gen_periodic | scalar | First k points of statrs' infinite periodic generator (sampling rate, frequency, amplitude, phase, delay) | NULL | [SELECT sr_gen_periodic(8, 8.0, 1.0, 1.0, 0.0, 0)] |
| sr_gen_sawtooth | scalar | First k points of statrs' infinite sawtooth wave (period as BIGINT) | NULL | [SELECT sr_gen_sawtooth(8, 4, 1.0, 0.0, 0)] |
| sr_gen_sinusoidal | scalar | First k points of statrs' infinite sinusoidal generator (sampling rate, frequency, amplitude, mean, phase, delay) | NULL | [SELECT sr_gen_sinusoidal(8, 8.0, 1.0, 1.0, 0.0, 0.0, 0)] |
| sr_gen_square | scalar | First k points of statrs' infinite square wave (high/low durations as BIGINT) | NULL | [SELECT sr_gen_square(8, 2, 2, 1.0, 0.0, 0)] |
| sr_gen_triangle | scalar | First k points of statrs' infinite triangle wave (raise/fall durations as BIGINT) | NULL | [SELECT sr_gen_triangle(8, 2, 2, 1.0, 0.0, 0)] |
| sr_generalized_harmonic | scalar | Generalized harmonic number sum of 1/k^m for k = 1..n, n as a UBIGINT and m real | NULL | [SELECT sr_generalized_harmonic(10, 2.0)] |
| sr_geometric_cdf | scalar | Geometric cumulative distribution function P(X <= x) | NULL | [SELECT sr_geometric_cdf(2, 0.5)] |
| sr_geometric_dist_mean | scalar | Mean of the Geometric distribution, 1/p (named _dist to avoid clashing with the sr_geometric_mean aggregate over a column) | NULL | [SELECT sr_geometric_dist_mean(0.5)] |
| sr_geometric_entropy | scalar | Geometric entropy | NULL | [SELECT sr_geometric_entropy(0.5)] |
| sr_geometric_ln_pmf | scalar | Geometric log probability mass at x | NULL | [SELECT sr_geometric_ln_pmf(2, 0.5)] |
| sr_geometric_max | scalar | Geometric maximum of the support (u64::MAX, shown as 1.8e19) | NULL | [SELECT sr_geometric_max(0.5)] |
| sr_geometric_mean | aggregate | Geometric mean of a DOUBLE column, NULL when a value is negative or no row is non-NULL | A negative value makes the statistic undefined, which comes back as NULL | [SELECT sr_geometric_mean(x) FROM (VALUES (1.0), (2.0), (3.0)) t(x)] |
| sr_geometric_median | scalar | Geometric median | NULL | [SELECT sr_geometric_median(0.5)] |
| sr_geometric_min | scalar | Geometric minimum of the support (1) | NULL | [SELECT sr_geometric_min(0.5)] |
| sr_geometric_mode | scalar | Geometric mode | NULL | [SELECT sr_geometric_mode(0.5)] |
| sr_geometric_pmf | scalar | Geometric probability mass P(X = x) for the number of trials until the first success (statrs' support starts at 1) | NULL | [SELECT sr_geometric_pmf(2, 0.5)] |
| sr_geometric_quantile | scalar | Geometric quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_geometric_quantile(0.5, 0.5)] |
| sr_geometric_sf | scalar | Geometric survival function P(X > x) | NULL | [SELECT sr_geometric_sf(2, 0.5)] |
| sr_geometric_skewness | scalar | Geometric skewness | NULL | [SELECT sr_geometric_skewness(0.5)] |
| sr_geometric_std_dev | scalar | Geometric standard deviation | NULL | [SELECT sr_geometric_std_dev(0.5)] |
| sr_geometric_variance | scalar | Geometric variance | NULL | [SELECT sr_geometric_variance(0.5)] |
| sr_gumbel_cdf | scalar | Gumbel cumulative distribution function P(X <= x) | NULL | [SELECT sr_gumbel_cdf(1.0, 0.0, 1.0)] |
| sr_gumbel_entropy | scalar | Gumbel (type-I extreme value) distribution differential entropy | NULL | [SELECT sr_gumbel_entropy(0.0, 1.0)] |
| sr_gumbel_ln_pdf | scalar | Gumbel log-density at x | NULL | [SELECT sr_gumbel_ln_pdf(1.0, 0.0, 1.0)] |
| sr_gumbel_max | scalar | Gumbel (type-I extreme value) distribution support maximum (positive infinity) | NULL | [SELECT sr_gumbel_max(0.0, 1.0)] |
| sr_gumbel_mean | scalar | Gumbel (type-I extreme value) distribution mean | NULL | [SELECT sr_gumbel_mean(0.0, 1.0)] |
| sr_gumbel_median | scalar | Gumbel (type-I extreme value) distribution median | NULL | [SELECT sr_gumbel_median(0.0, 1.0)] |
| sr_gumbel_min | scalar | Gumbel (type-I extreme value) distribution support minimum (negative infinity) | NULL | [SELECT sr_gumbel_min(0.0, 1.0)] |
| sr_gumbel_mode | scalar | Gumbel (type-I extreme value) distribution mode | NULL | [SELECT sr_gumbel_mode(0.0, 1.0)] |
| sr_gumbel_pdf | scalar | Gumbel (type-I extreme value) probability density at x, given location and scale | NULL | [SELECT sr_gumbel_pdf(1.0, 0.0, 1.0)] |
| sr_gumbel_quantile | scalar | Gumbel quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_gumbel_quantile(0.5, 0.0, 1.0)] |
| sr_gumbel_sf | scalar | Gumbel survival function P(X > x) | NULL | [SELECT sr_gumbel_sf(1.0, 0.0, 1.0)] |
| sr_gumbel_skewness | scalar | Gumbel (type-I extreme value) distribution skewness | NULL | [SELECT sr_gumbel_skewness(0.0, 1.0)] |
| sr_gumbel_std_dev | scalar | Gumbel (type-I extreme value) distribution standard deviation | NULL | [SELECT sr_gumbel_std_dev(0.0, 1.0)] |
| sr_gumbel_variance | scalar | Gumbel (type-I extreme value) distribution variance | NULL | [SELECT sr_gumbel_variance(0.0, 1.0)] |
| sr_harmonic | scalar | Harmonic number H(n) = sum of 1/k for k = 1..n, n as a UBIGINT | NULL | [SELECT sr_harmonic(10)] |
| sr_harmonic_mean | aggregate | Harmonic mean of a DOUBLE column, NULL when a value is negative or no row is non-NULL | A negative value makes the statistic undefined, which comes back as NULL | [SELECT sr_harmonic_mean(x) FROM (VALUES (1.0), (2.0), (3.0)) t(x)] |
| sr_hypergeometric_cdf | scalar | Hypergeometric cumulative distribution function P(X <= x) | NULL | [SELECT sr_hypergeometric_cdf(2, 10, 5, 4)] |
| sr_hypergeometric_entropy | scalar | Hypergeometric entropy | NULL | [SELECT sr_hypergeometric_entropy(10, 5, 4)] |
| sr_hypergeometric_ln_pmf | scalar | Hypergeometric log probability mass at x | NULL | [SELECT sr_hypergeometric_ln_pmf(2, 10, 5, 4)] |
| sr_hypergeometric_max | scalar | Hypergeometric maximum of the support | NULL | [SELECT sr_hypergeometric_max(10, 5, 4)] |
| sr_hypergeometric_mean | scalar | Hypergeometric mean | NULL | [SELECT sr_hypergeometric_mean(10, 5, 4)] |
| sr_hypergeometric_min | scalar | Hypergeometric minimum of the support | NULL | [SELECT sr_hypergeometric_min(10, 5, 4)] |
| sr_hypergeometric_mode | scalar | Hypergeometric mode | NULL | [SELECT sr_hypergeometric_mode(10, 5, 4)] |
| sr_hypergeometric_pmf | scalar | Hypergeometric probability mass P(X = x): successes drawn without replacement (population, successes, draws as UBIGINT) | NULL | [SELECT sr_hypergeometric_pmf(2, 10, 5, 4)] |
| sr_hypergeometric_quantile | scalar | Hypergeometric quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_hypergeometric_quantile(0.5, 10, 5, 4)] |
| sr_hypergeometric_sf | scalar | Hypergeometric survival function P(X > x) | NULL | [SELECT sr_hypergeometric_sf(2, 10, 5, 4)] |
| sr_hypergeometric_skewness | scalar | Hypergeometric skewness | NULL | [SELECT sr_hypergeometric_skewness(10, 5, 4)] |
| sr_hypergeometric_std_dev | scalar | Hypergeometric standard deviation | NULL | [SELECT sr_hypergeometric_std_dev(10, 5, 4)] |
| sr_hypergeometric_variance | scalar | Hypergeometric variance | NULL | [SELECT sr_hypergeometric_variance(10, 5, 4)] |
| sr_interquartile_range | aggregate | Interquartile range of a DOUBLE column, NULL when no row is non-NULL | NULL | [SELECT sr_interquartile_range(x) FROM (VALUES (2.0), (1.0), (3.0), (4.0)) t(x)] |
| sr_inv_beta_regularized | scalar | Inverse of the regularized incomplete Beta function: the x where I(x; a, b) = p | NULL | [SELECT sr_inv_beta_regularized(2.0, 3.0, 0.6875)] |
| sr_inv_digamma | scalar | Inverse digamma function, ψ(x) = y solved for x | NULL | [SELECT sr_inv_digamma(0.42278433509846713)] |
| sr_inverse_gamma_cdf | scalar | Inverse-gamma cumulative distribution function P(X <= x) | NULL | [SELECT sr_inverse_gamma_cdf(1.0, 2.0, 2.0)] |
| sr_inverse_gamma_entropy | scalar | Inverse-gamma differential entropy, given shape and scale | NULL | [SELECT sr_inverse_gamma_entropy(2.0, 1.0)] |
| sr_inverse_gamma_ln_pdf | scalar | Inverse-gamma log-density at x | NULL | [SELECT sr_inverse_gamma_ln_pdf(1.0, 2.0, 2.0)] |
| sr_inverse_gamma_max | scalar | Inverse-gamma maximum of the support (positive infinity) | NULL | [SELECT sr_inverse_gamma_max(2.0, 1.0)] |
| sr_inverse_gamma_mean | scalar | Inverse-gamma mean, given shape and scale | NULL | [SELECT sr_inverse_gamma_mean(2.0, 1.0)] |
| sr_inverse_gamma_min | scalar | Inverse-gamma minimum of the support (0) | NULL | [SELECT sr_inverse_gamma_min(2.0, 1.0)] |
| sr_inverse_gamma_mode | scalar | Inverse-gamma mode, given shape and scale | NULL | [SELECT sr_inverse_gamma_mode(2.0, 1.0)] |
| sr_inverse_gamma_pdf | scalar | Inverse-gamma probability density at x, given shape and scale | NULL | [SELECT sr_inverse_gamma_pdf(1.0, 2.0, 2.0)] |
| sr_inverse_gamma_quantile | scalar | Inverse-gamma quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_inverse_gamma_quantile(0.5, 2.0, 2.0)] |
| sr_inverse_gamma_sf | scalar | Inverse-gamma survival function P(X > x) | NULL | [SELECT sr_inverse_gamma_sf(1.0, 2.0, 2.0)] |
| sr_inverse_gamma_skewness | scalar | Inverse-gamma skewness, given shape and scale | NULL | [SELECT sr_inverse_gamma_skewness(4.0, 1.0)] |
| sr_inverse_gamma_std_dev | scalar | Inverse-gamma standard deviation, given shape and scale | NULL | [SELECT sr_inverse_gamma_std_dev(3.0, 1.0)] |
| sr_inverse_gamma_variance | scalar | Inverse-gamma variance, given shape and scale | NULL | [SELECT sr_inverse_gamma_variance(3.0, 1.0)] |
| sr_kde_pdf | scalar | Kernel density estimate at x from a LIST(DOUBLE) sample; NULL bandwidth selects statrs' automatic bandwidth | Gaussian kernel over a k-d tree; errors (empty sample, empty neighbourhood) fail the query | [SELECT sr_kde_pdf(0.5, [0.0, 0.2, 0.7, 1.0], 0.3)] |
| sr_kernel_eval | scalar | Kernel function evaluation K(x) for a named kernel (gaussian, epanechnikov, triangular, tricube, quartic, uniform, cosine, logistic, sigmoid; case-insensitive) | NULL | [SELECT sr_kernel_eval('gaussian', 0.0)] |
| sr_kernel_eval_with_bandwidth | scalar | Kernel function with bandwidth scaling K(x / h) / h, for a named kernel (same names as sr_kernel_eval) | NULL | [SELECT sr_kernel_eval_with_bandwidth('gaussian', 0.0, 0.5)] |
| sr_kernel_support | scalar | Compact support [lo, hi] of a named kernel (same names as sr_kernel_eval); NULL for kernels with unbounded support | NULL | [SELECT sr_kernel_support('epanechnikov')] |
| sr_knn_pdf | scalar | K-nearest-neighbour density estimate at x from a LIST(DOUBLE) sample; NULL bandwidth selects the automatic k | NULL | [SELECT sr_knn_pdf(0.5, [0.0, 0.2, 0.7, 1.0], 0.3)] |
| sr_ks_onesample | scalar | One-sample Kolmogorov-Smirnov test of a LIST(DOUBLE) sample against a named distribution (normal / lognormal / exponential / gumbel / weibull / uniform) with its parameter LIST: LIST [KS statistic, p-value]; method 1 less 2 greater 3 two-sided exact 4 two-sided asymptotic 5 two-sided approximate | NULL | [SELECT sr_ks_onesample([1.0, 2.0, 3.0, 4.0], 'normal', [2.5, 1.0], 4.0, 1.0)] |
| sr_ks_twosample | scalar | Two-sample Kolmogorov-Smirnov test of two LIST(DOUBLE) samples: LIST [KS distance, p-value]; method 1 less 2 greater (asymptotic), 3 two-sided exact, 4 two-sided asymptotic | NULL | [SELECT sr_ks_twosample([1.0, 2.0, 3.0], [2.0, 3.0, 4.0], 4.0, 1.0)] |
| sr_laplace_cdf | scalar | Laplace cumulative distribution function P(X <= x) | NULL | [SELECT sr_laplace_cdf(1.0, 0.0, 1.0)] |
| sr_laplace_entropy | scalar | Laplace distribution differential entropy | NULL | [SELECT sr_laplace_entropy(0.0, 1.0)] |
| sr_laplace_ln_pdf | scalar | Laplace log-density at x | NULL | [SELECT sr_laplace_ln_pdf(1.0, 0.0, 1.0)] |
| sr_laplace_max | scalar | Laplace distribution support maximum (positive infinity) | NULL | [SELECT sr_laplace_max(0.0, 1.0)] |
| sr_laplace_mean | scalar | Laplace distribution mean | NULL | [SELECT sr_laplace_mean(0.0, 1.0)] |
| sr_laplace_median | scalar | Laplace distribution median | NULL | [SELECT sr_laplace_median(0.0, 1.0)] |
| sr_laplace_min | scalar | Laplace distribution support minimum (negative infinity) | NULL | [SELECT sr_laplace_min(0.0, 1.0)] |
| sr_laplace_mode | scalar | Laplace distribution mode | NULL | [SELECT sr_laplace_mode(0.0, 1.0)] |
| sr_laplace_pdf | scalar | Laplace probability density at x, given location and scale | NULL | [SELECT sr_laplace_pdf(1.0, 0.0, 1.0)] |
| sr_laplace_quantile | scalar | Laplace quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_laplace_quantile(0.5, 0.0, 1.0)] |
| sr_laplace_sf | scalar | Laplace survival function P(X > x) | NULL | [SELECT sr_laplace_sf(1.0, 0.0, 1.0)] |
| sr_laplace_skewness | scalar | Laplace distribution skewness (always 0) | NULL | [SELECT sr_laplace_skewness(0.0, 1.0)] |
| sr_laplace_std_dev | scalar | Laplace distribution standard deviation | NULL | [SELECT sr_laplace_std_dev(0.0, 1.0)] |
| sr_laplace_variance | scalar | Laplace distribution variance | NULL | [SELECT sr_laplace_variance(0.0, 1.0)] |
| sr_levy_cdf | scalar | Lévy cumulative distribution function P(X <= x) | NULL | [SELECT sr_levy_cdf(1.0, 0.0, 1.0)] |
| sr_levy_entropy | scalar | Lévy distribution differential entropy | NULL | [SELECT sr_levy_entropy(0.0, 1.0)] |
| sr_levy_ln_pdf | scalar | Lévy log-density at x | NULL | [SELECT sr_levy_ln_pdf(1.0, 0.0, 1.0)] |
| sr_levy_max | scalar | Lévy distribution support maximum (positive infinity) | NULL | [SELECT sr_levy_max(0.0, 1.0)] |
| sr_levy_mean | scalar | Lévy distribution mean (undefined) | NULL | [SELECT sr_levy_mean(0.0, 1.0)] |
| sr_levy_median | scalar | Lévy distribution median | NULL | [SELECT sr_levy_median(0.0, 1.0)] |
| sr_levy_min | scalar | Lévy distribution support minimum (mu) | NULL | [SELECT sr_levy_min(0.0, 1.0)] |
| sr_levy_mode | scalar | Lévy distribution mode | NULL | [SELECT sr_levy_mode(0.0, 1.0)] |
| sr_levy_pdf | scalar | Lévy probability density at x, given location mu and scale c | NULL | [SELECT sr_levy_pdf(1.0, 0.0, 1.0)] |
| sr_levy_quantile | scalar | Lévy quantile function: the x whose CDF equals p, for p in [0, 1] | statrs solves this one numerically (bisection), accuracy is lower than the closed forms | [SELECT sr_levy_quantile(0.5, 0.0, 1.0)] |
| sr_levy_sf | scalar | Lévy survival function P(X > x) | NULL | [SELECT sr_levy_sf(1.0, 0.0, 1.0)] |
| sr_levy_skewness | scalar | Lévy distribution skewness (undefined) | NULL | [SELECT sr_levy_skewness(0.0, 1.0)] |
| sr_levy_std_dev | scalar | Lévy distribution standard deviation (undefined) | NULL | [SELECT sr_levy_std_dev(0.0, 1.0)] |
| sr_levy_variance | scalar | Lévy distribution variance (undefined) | NULL | [SELECT sr_levy_variance(0.0, 1.0)] |
| sr_ln_2_sqrt_e_over_pi | scalar | The constant ln(2*sqrt(e/PI)) | NULL | [SELECT sr_ln_2_sqrt_e_over_pi()] |
| sr_ln_beta | scalar | Natural logarithm of the Beta function, ln(B(a, b)) | NULL | [SELECT sr_ln_beta(2.0, 3.0)] |
| sr_ln_choose | scalar | Natural logarithm of the binomial coefficient C(n, k), n and k UBIGINTs | NULL | [SELECT sr_ln_choose(100, 50)] |
| sr_ln_factorial | scalar | Natural logarithm of n!, n as a UBIGINT | NULL | [SELECT sr_ln_factorial(100)] |
| sr_ln_gamma | scalar | Natural logarithm of the Gamma function, ln(Γ(x)) | NULL | [SELECT sr_ln_gamma(5.0)] |
| sr_ln_pi | scalar | The constant ln(PI) | NULL | [SELECT sr_ln_pi()] |
| sr_ln_sqrt_2pi | scalar | The constant ln(sqrt(2*PI)) | NULL | [SELECT sr_ln_sqrt_2pi()] |
| sr_ln_sqrt_2pie | scalar | The constant ln(sqrt(2PIe)) | NULL | [SELECT sr_ln_sqrt_2pie()] |
| sr_log_normal_cdf | scalar | Log-normal cumulative distribution function P(X <= x) | NULL | [SELECT sr_log_normal_cdf(1.0, 0.0, 1.0)] |
| sr_log_normal_entropy | scalar | Log-normal distribution differential entropy | NULL | [SELECT sr_log_normal_entropy(0.0, 1.0)] |
| sr_log_normal_ln_pdf | scalar | Log-normal log-density at x | NULL | [SELECT sr_log_normal_ln_pdf(1.0, 0.0, 1.0)] |
| sr_log_normal_max | scalar | Log-normal distribution support maximum (positive infinity) | NULL | [SELECT sr_log_normal_max(0.0, 1.0)] |
| sr_log_normal_mean | scalar | Log-normal distribution mean | NULL | [SELECT sr_log_normal_mean(0.0, 1.0)] |
| sr_log_normal_median | scalar | Log-normal distribution median | NULL | [SELECT sr_log_normal_median(0.0, 1.0)] |
| sr_log_normal_min | scalar | Log-normal distribution support minimum (0) | NULL | [SELECT sr_log_normal_min(0.0, 1.0)] |
| sr_log_normal_mode | scalar | Log-normal distribution mode | NULL | [SELECT sr_log_normal_mode(0.0, 1.0)] |
| sr_log_normal_pdf | scalar | Log-normal probability density at x (location and scale of ln X) | NULL | [SELECT sr_log_normal_pdf(1.0, 0.0, 1.0)] |
| sr_log_normal_quantile | scalar | Log-normal quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_log_normal_quantile(0.5, 0.0, 1.0)] |
| sr_log_normal_sf | scalar | Log-normal survival function P(X > x) | NULL | [SELECT sr_log_normal_sf(1.0, 0.0, 1.0)] |
| sr_log_normal_skewness | scalar | Log-normal distribution skewness | NULL | [SELECT sr_log_normal_skewness(0.0, 1.0)] |
| sr_log_normal_std_dev | scalar | Log-normal distribution standard deviation | NULL | [SELECT sr_log_normal_std_dev(0.0, 1.0)] |
| sr_log_normal_variance | scalar | Log-normal distribution variance | NULL | [SELECT sr_log_normal_variance(0.0, 1.0)] |
| sr_logistic | scalar | Logistic (sigmoid) function 1 / (1 + exp(-p)) | NULL | [SELECT sr_logistic(0.0)] |
| sr_logit | scalar | Logit, the inverse sigmoid ln(p / (1 - p)); NULL unless p is in [0, 1], endpoints give infinity | NULL | [SELECT sr_logit(0.5)] |
| sr_lower_quartile | aggregate | First quartile (lower hinge) of a DOUBLE column, NULL when no row is non-NULL | NULL | [SELECT sr_lower_quartile(x) FROM (VALUES (2.0), (1.0), (3.0), (4.0)) t(x)] |
| sr_mannwhitneyu | scalar | Mann-Whitney U test of two LIST(DOUBLE) samples: LIST [U statistic, p-value]; method 1 automatic 2 exact 3 asymptotic incl. continuity correction 4 excl., plus the alternative codes | NULL | [SELECT sr_mannwhitneyu([1.0, 2.0, 3.0], [2.0, 3.0, 4.0], 1.0, 1.0)] |
| sr_max | aggregate | Maximum of a DOUBLE column (statrs' Statistics::max), NULL when no row is non-NULL | NULL | [SELECT sr_max(x) FROM (VALUES (0.0), (3.0), (-2.0)) t(x)] |
| sr_max_factorial | scalar | The maximum n such that factorial(n) does not overflow to infinity (statrs' factorial::MAX_FACTORIAL, as a UBIGINT) | NULL | [SELECT sr_max_factorial()] |
| sr_mean | aggregate | Arithmetic mean of a DOUBLE column, NULL when no row is non-NULL | SQL NULL rows are skipped; statrs' NAN for an empty group becomes SQL NULL | [SELECT sr_mean(x) FROM (VALUES (1.0), (2.0), (3.0)) t(x)] |
| sr_median | aggregate | Median of a DOUBLE column, NULL when no row is non-NULL | Even-length inputs average the two middle values, statrs' own convention | [SELECT sr_median(x) FROM (VALUES (3.0), (1.0), (2.0)) t(x)] |
| sr_min | aggregate | Minimum of a DOUBLE column (statrs' Statistics::min), NULL when no row is non-NULL | NULL | [SELECT sr_min(x) FROM (VALUES (0.0), (3.0), (-2.0)) t(x)] |
| sr_modulus | scalar | Canonical (Euclidean) modulus for f32, always in [0, divisor); NULL for a zero divisor | NULL | [SELECT sr_modulus(-1.0, 5.0)] |
| sr_multinomial_coefficient | scalar | Multinomial coefficient n! / (n1! n2! …) over a UBIGINT n and a count LIST(UBIGINT); NULL when the counts do not sum to n | NULL | [SELECT sr_multinomial_coefficient(5, [2, 2, 1])] |
| sr_multinomial_ln_pmf | scalar | Log probability mass of a count LIST(UBIGINT) under the multinomial distribution; -inf when the counts do not sum to n | NULL | [SELECT sr_multinomial_ln_pmf([0.5, 0.5], 2000, [1000, 1000])] |
| sr_multinomial_mean | scalar | Mean vector of the multinomial distribution (n * p_i) given category probabilities and the trial count (UBIGINT) | NULL | [SELECT sr_multinomial_mean([0.3, 0.7], 5)] |
| sr_multinomial_pmf | scalar | Multinomial probability mass of a count LIST(UBIGINT), given category probabilities and the trial count (UBIGINT) | NULL | [SELECT sr_multinomial_pmf([1.0, 2.0], 3, [1, 2])] |
| sr_multinomial_variance | scalar | Covariance matrix of the multinomial distribution (row-major flattened LIST) given category probabilities and the trial count (UBIGINT) | NULL | [SELECT sr_multinomial_variance([0.1, 0.3, 0.6], 10)] |
| sr_multivariate_normal_entropy | scalar | Differential entropy of the multivariate normal distribution given the mean and a row-major flattened covariance matrix | NULL | [SELECT sr_multivariate_normal_entropy([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_ln_pdf | scalar | Log probability density of x under a multivariate normal distribution with the given mean and a row-major flattened covariance matrix | NULL | [SELECT sr_multivariate_normal_ln_pdf([1.0, 1.0], [0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_max | scalar | Upper bound of the multivariate normal support: a vector of +inf with the dimension of the mean | NULL | [SELECT sr_multivariate_normal_max([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_mean | scalar | Mean vector of the multivariate normal distribution given the mean and a row-major flattened covariance matrix | NULL | [SELECT sr_multivariate_normal_mean([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_min | scalar | Lower bound of the multivariate normal support: a vector of -inf with the dimension of the mean | NULL | [SELECT sr_multivariate_normal_min([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_mode | scalar | Mode vector of the multivariate normal distribution given the mean and a row-major flattened covariance matrix | NULL | [SELECT sr_multivariate_normal_mode([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_pdf | scalar | Multivariate normal probability density of x (LIST) given the mean and a row-major flattened covariance matrix | NULL | [SELECT sr_multivariate_normal_pdf([0.0, 0.0], [0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_precision | scalar | Precision matrix (inverse of the covariance matrix, row-major flattened LIST) of the multivariate normal distribution | NULL | [SELECT sr_multivariate_normal_precision([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_normal_variance | scalar | Covariance matrix of the multivariate normal distribution (row-major flattened LIST) given the mean and a row-major flattened covariance matrix | NULL | [SELECT sr_multivariate_normal_variance([0.0, 0.0], [1.0, 0.0, 0.0, 1.0])] |
| sr_multivariate_students_t_ln_pdf | scalar | Log probability density of x under a multivariate Student's t distribution, given location, a row-major flattened scale matrix and the degrees of freedom | NULL | [SELECT sr_multivariate_students_t_ln_pdf([1.0, 1.0], [0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 4.0)] |
| sr_multivariate_students_t_max | scalar | Upper bound of the multivariate Student's t support: a vector of +inf with the dimension of the location | NULL | [SELECT sr_multivariate_students_t_max([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0)] |
| sr_multivariate_students_t_mean | scalar | Mean vector of the multivariate Student's t distribution; NULL when the degrees of freedom is at most 1 | NULL | [SELECT sr_multivariate_students_t_mean([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 2.0)] |
| sr_multivariate_students_t_min | scalar | Lower bound of the multivariate Student's t support: a vector of -inf with the dimension of the location | NULL | [SELECT sr_multivariate_students_t_min([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0)] |
| sr_multivariate_students_t_mode | scalar | Mode vector of the multivariate Student's t distribution given location, a row-major flattened scale matrix and the degrees of freedom | NULL | [SELECT sr_multivariate_students_t_mode([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0)] |
| sr_multivariate_students_t_pdf | scalar | Multivariate Student's t probability density of x, given location, a row-major flattened scale matrix and the degrees of freedom | NULL | [SELECT sr_multivariate_students_t_pdf([0.0, 0.0], [0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0)] |
| sr_multivariate_students_t_precision | scalar | Precision matrix (inverse of the scale matrix, row-major flattened LIST) of the multivariate Student's t distribution | NULL | [SELECT sr_multivariate_students_t_precision([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0)] |
| sr_multivariate_students_t_variance | scalar | Covariance matrix (row-major flattened LIST) of the multivariate Student's t distribution, scale * nu/(nu-2); NULL when the degrees of freedom is at most 2 | NULL | [SELECT sr_multivariate_students_t_variance([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0)] |
| sr_negative_binomial_cdf | scalar | Negative-binomial cumulative distribution function P(X <= x) | NULL | [SELECT sr_negative_binomial_cdf(3, 2.0, 0.5)] |
| sr_negative_binomial_entropy | scalar | Negative-binomial entropy | NULL | [SELECT sr_negative_binomial_entropy(2.0, 0.5)] |
| sr_negative_binomial_ln_pmf | scalar | Negative-binomial log probability mass at x | NULL | [SELECT sr_negative_binomial_ln_pmf(3, 2.0, 0.5)] |
| sr_negative_binomial_max | scalar | Negative-binomial maximum of the support (u64::MAX, shown as 1.8e19) | NULL | [SELECT sr_negative_binomial_max(2.0, 0.5)] |
| sr_negative_binomial_mean | scalar | Negative-binomial mean | NULL | [SELECT sr_negative_binomial_mean(2.0, 0.5)] |
| sr_negative_binomial_min | scalar | Negative-binomial minimum of the support (0) | NULL | [SELECT sr_negative_binomial_min(2.0, 0.5)] |
| sr_negative_binomial_mode | scalar | Negative-binomial mode (statrs returns a real-valued Option |
NULL | [SELECT sr_negative_binomial_mode(2.0, 0.5)] |
| sr_negative_binomial_pmf | scalar | Negative-binomial probability mass P(X = x): failures before the r-th success (real r, success probability p) | NULL | [SELECT sr_negative_binomial_pmf(3, 2.0, 0.5)] |
| sr_negative_binomial_quantile | scalar | Negative-binomial quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_negative_binomial_quantile(0.5, 2.0, 0.5)] |
| sr_negative_binomial_sf | scalar | Negative-binomial survival function P(X > x) | NULL | [SELECT sr_negative_binomial_sf(3, 2.0, 0.5)] |
| sr_negative_binomial_skewness | scalar | Negative-binomial skewness | NULL | [SELECT sr_negative_binomial_skewness(2.0, 0.5)] |
| sr_negative_binomial_std_dev | scalar | Negative-binomial standard deviation | NULL | [SELECT sr_negative_binomial_std_dev(2.0, 0.5)] |
| sr_negative_binomial_variance | scalar | Negative-binomial variance | NULL | [SELECT sr_negative_binomial_variance(2.0, 0.5)] |
| sr_normal_cdf | scalar | Normal (Gaussian) cumulative distribution function P(X <= x) | NULL | [SELECT sr_normal_cdf(1.96, 0.0, 1.0)] |
| sr_normal_entropy | scalar | Normal (Gaussian) distribution differential entropy | NULL | [SELECT sr_normal_entropy(0.0, 1.0)] |
| sr_normal_ln_pdf | scalar | Normal (Gaussian) log-density at x, given mean and standard deviation | NULL | [SELECT sr_normal_ln_pdf(0.0, 0.0, 1.0)] |
| sr_normal_max | scalar | Normal (Gaussian) distribution support maximum (positive infinity) | NULL | [SELECT sr_normal_max(0.0, 1.0)] |
| sr_normal_mean | scalar | Normal (Gaussian) distribution mean | NULL | [SELECT sr_normal_mean(0.0, 1.0)] |
| sr_normal_median | scalar | Normal (Gaussian) distribution median | NULL | [SELECT sr_normal_median(0.0, 1.0)] |
| sr_normal_min | scalar | Normal (Gaussian) distribution support minimum (negative infinity) | NULL | [SELECT sr_normal_min(0.0, 1.0)] |
| sr_normal_mode | scalar | Normal (Gaussian) distribution mode | NULL | [SELECT sr_normal_mode(0.0, 1.0)] |
| sr_normal_pdf | scalar | Normal (Gaussian) probability density at x, given mean and standard deviation | NULL | [SELECT sr_normal_pdf(0.0, 0.0, 1.0)] |
| sr_normal_quantile | scalar | Normal (Gaussian) quantile function: the x whose CDF equals p, for p in [0, 1] | A probability outside [0, 1] is a query error rather than a clamped endpoint | [SELECT sr_normal_quantile(0.975, 0.0, 1.0)] |
| sr_normal_sf | scalar | Normal (Gaussian) survival function P(X > x) | NULL | [SELECT sr_normal_sf(1.96, 0.0, 1.0)] |
| sr_normal_skewness | scalar | Normal (Gaussian) distribution skewness (always 0) | NULL | [SELECT sr_normal_skewness(0.0, 1.0)] |
| sr_normal_std_dev | scalar | Normal (Gaussian) distribution standard deviation | NULL | [SELECT sr_normal_std_dev(0.0, 1.0)] |
| sr_normal_variance | scalar | Normal (Gaussian) distribution variance | NULL | [SELECT sr_normal_variance(0.0, 1.0)] |
| sr_order_statistic | aggregate | k-th smallest value of a DOUBLE column (1-based, k as UBIGINT), NULL when k is outside the data range | NULL | [SELECT sr_order_statistic(x, 2) FROM (VALUES (3.0), (1.0), (2.0)) t(x)] |
| sr_pareto_cdf | scalar | Pareto cumulative distribution function P(X <= x) | NULL | [SELECT sr_pareto_cdf(2.0, 1.0, 2.0)] |
| sr_pareto_entropy | scalar | Pareto (type-I) differential entropy, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_entropy(1.0, 2.0)] |
| sr_pareto_ln_pdf | scalar | Pareto log-density at x | NULL | [SELECT sr_pareto_ln_pdf(1.0, 1.0, 2.0)] |
| sr_pareto_max | scalar | Pareto (type-I) maximum of the support (positive infinity) | NULL | [SELECT sr_pareto_max(1.0, 2.0)] |
| sr_pareto_mean | scalar | Pareto (type-I) mean, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_mean(1.0, 2.0)] |
| sr_pareto_median | scalar | Pareto (type-I) median, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_median(1.0, 2.0)] |
| sr_pareto_min | scalar | Pareto (type-I) minimum of the support (the scale) | NULL | [SELECT sr_pareto_min(1.0, 2.0)] |
| sr_pareto_mode | scalar | Pareto (type-I) mode, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_mode(1.0, 2.0)] |
| sr_pareto_pdf | scalar | Pareto (type-I) probability density at x, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_pdf(1.0, 1.0, 2.0)] |
| sr_pareto_quantile | scalar | Pareto quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_pareto_quantile(0.5, 1.0, 2.0)] |
| sr_pareto_sf | scalar | Pareto survival function P(X > x) | NULL | [SELECT sr_pareto_sf(2.0, 1.0, 2.0)] |
| sr_pareto_skewness | scalar | Pareto (type-I) skewness, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_skewness(1.0, 4.0)] |
| sr_pareto_std_dev | scalar | Pareto (type-I) standard deviation, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_std_dev(1.0, 3.0)] |
| sr_pareto_variance | scalar | Pareto (type-I) variance, given scale x_m and shape alpha | NULL | [SELECT sr_pareto_variance(1.0, 3.0)] |
| sr_percentile | aggregate | p-th percentile of a DOUBLE column (p as a UBIGINT in 0..=100), NULL when out of range | Use sr_quantile for non-integer positions | [SELECT sr_percentile(x, 50) FROM (VALUES (1.0), (2.0), (3.0), (4.0)) t(x)] |
| sr_poisson_cdf | scalar | Poisson cumulative distribution function P(X <= x) | NULL | [SELECT sr_poisson_cdf(2, 3.0)] |
| sr_poisson_entropy | scalar | Poisson entropy | NULL | [SELECT sr_poisson_entropy(3.0)] |
| sr_poisson_ln_pmf | scalar | Poisson log probability mass at x | NULL | [SELECT sr_poisson_ln_pmf(2, 3.0)] |
| sr_poisson_max | scalar | Poisson maximum of the support (u64::MAX, shown as 1.8e19) | NULL | [SELECT sr_poisson_max(3.0)] |
| sr_poisson_mean | scalar | Poisson mean | NULL | [SELECT sr_poisson_mean(3.0)] |
| sr_poisson_median | scalar | Poisson median | NULL | [SELECT sr_poisson_median(3.0)] |
| sr_poisson_min | scalar | Poisson minimum of the support (0) | NULL | [SELECT sr_poisson_min(3.0)] |
| sr_poisson_mode | scalar | Poisson mode | NULL | [SELECT sr_poisson_mode(3.0)] |
| sr_poisson_pmf | scalar | Poisson probability mass P(X = x), given the rate lambda | NULL | [SELECT sr_poisson_pmf(2, 3.0)] |
| sr_poisson_quantile | scalar | Poisson quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_poisson_quantile(0.5, 3.0)] |
| sr_poisson_sf | scalar | Poisson survival function P(X > x) | NULL | [SELECT sr_poisson_sf(2, 3.0)] |
| sr_poisson_skewness | scalar | Poisson skewness | NULL | [SELECT sr_poisson_skewness(3.0)] |
| sr_poisson_std_dev | scalar | Poisson standard deviation | NULL | [SELECT sr_poisson_std_dev(3.0)] |
| sr_poisson_variance | scalar | Poisson variance | NULL | [SELECT sr_poisson_variance(3.0)] |
| sr_polynomial | scalar | Polynomial evaluation sum coeff[i] * x^i with the coefficient LIST in ascending order | NULL | [SELECT sr_polynomial(2.0, [1.0, 0.0, 3.0])] |
| sr_population_covariance | aggregate | Population covariance of two DOUBLE columns, NULL when no row is fully non-NULL | A row with a NULL in either column is skipped entirely, keeping the two columns paired | [SELECT sr_population_covariance(x, y) FROM (VALUES (0.0, -5.0), (3.0, 4.0), (-2.0, 10.0)) t(x, y)] |
| sr_population_std_dev | aggregate | Population standard deviation of a DOUBLE column, NULL when no row is non-NULL | Single-row groups yield a real number here (dividing by N), unlike the sample family | [SELECT sr_population_std_dev(x) FROM (VALUES (0.0), (3.0), (-2.0)) t(x)] |
| sr_population_variance | aggregate | Population variance of a DOUBLE column, NULL when no row is non-NULL | Single-row groups yield a real number here (dividing by N), unlike the sample family | [SELECT sr_population_variance(x) FROM (VALUES (0.0), (3.0), (-2.0)) t(x)] |
| sr_quadratic_mean | aggregate | Quadratic mean (root mean square) of a DOUBLE column, NULL when no row is non-NULL | SQL NULL rows are skipped; statrs' NAN for an empty group becomes SQL NULL | [SELECT sr_quadratic_mean(x) FROM (VALUES (1.0), (2.0), (3.0)) t(x)] |
| sr_quantile | aggregate | Tau quantile of a DOUBLE column, tau as the second (constant) argument, NULL when empty or tau is not in [0, 1] | Write the tau argument as a literal; a NULL tau skips the row entirely, like any NULL input | [SELECT sr_quantile(x, 0.5) FROM (VALUES (1.0), (2.0), (3.0), (4.0)) t(x)] |
| sr_ranks | aggregate | Ranks of a DOUBLE column as LIST(DOUBLE); method 1=average 2=min 3=max 4=first (statrs' tie breakers) | Ties follow the chosen RankTieBreaker; an out-of-range method is a query error | [SELECT sr_ranks(x, 1.0) FROM (VALUES (1.0), (3.0), (2.0), (2.0)) t(x)] |
| sr_sample_bernoulli | scalar | Draw k Bernoulli(p) samples (0/1) into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_bernoulli(0.5, 10))] |
| sr_sample_beta | scalar | Draw k Beta(shape_a, shape_b) samples into a LIST(DOUBLE) using statrs' rand integration | NULL | [SELECT len(sr_sample_beta(2.0, 3.0, 10))] |
| sr_sample_binomial | scalar | Draw k Binomial(p, UBIGINT n) samples into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_binomial(0.5, 10, 8))] |
| sr_sample_binomial_algorithm | scalar | Draw k Binomial(p, n) samples through statrs' BinomialSampler with an explicit algorithm (1 automatic, 2 inversion, 3 rejection) into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_binomial_algorithm(0.5, 10, 1.0, 8))] |
| sr_sample_categorical | scalar | Draw k Categorical(prob LIST) samples as category indices into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_categorical([1.0, 2.0, 1.0], 10))] |
| sr_sample_cauchy | scalar | Draw k Cauchy(location, scale) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_cauchy(0.0, 1.0, 10))] |
| sr_sample_chi | scalar | Draw k Chi(UBIGINT freedom) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_chi(2, 10))] |
| sr_sample_chi_squared | scalar | Draw k Chi-squared(freedom) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_chi_squared(2.0, 10))] |
| sr_sample_dirac | scalar | Draw k Dirac(v) samples into a LIST(DOUBLE) | NULL | [SELECT sr_sample_dirac(3.0, 2)] |
| sr_sample_dirichlet | scalar | Draw k Dirichlet samples on the simplex (concentration LIST alpha) as a LIST of point LISTs, each summing to 1 | NULL | [SELECT len(sr_sample_dirichlet([1.0, 2.0], 4))] |
| sr_sample_discrete_uniform | scalar | Draw k DiscreteUniform(BIGINT min, max) samples into a LIST(BIGINT) | NULL | [SELECT len(sr_sample_discrete_uniform(1, 6, 10))] |
| sr_sample_empirical | aggregate | Draw k samples from the empirical distribution of a DOUBLE column into a LIST(DOUBLE); k is the second (constant) argument | NULL | [SELECT sr_sample_empirical(v, 5) FROM (VALUES (1.0), (2.0), (3.0)) t(v)] |
| sr_sample_erlang | scalar | Draw k Erlang(UBIGINT shape, DOUBLE rate) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_erlang(2, 2.0, 10))] |
| sr_sample_exp | scalar | Draw k Exponential(rate) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_exp(2.0, 10))] |
| sr_sample_fisher_snedecor | scalar | Draw k Fisher-Snedecor(f1, f2) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_fisher_snedecor(2.0, 3.0, 10))] |
| sr_sample_gamma | scalar | Draw k Gamma(shape, rate) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_gamma(2.0, 2.0, 10))] |
| sr_sample_geometric | scalar | Draw k Geometric(p) samples into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_geometric(0.5, 10))] |
| sr_sample_gumbel | scalar | Draw k Gumbel(location, scale) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_gumbel(0.0, 1.0, 10))] |
| sr_sample_hypergeometric | scalar | Draw k Hypergeometric(population, successes, draws as UBIGINT) samples into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_hypergeometric(10, 5, 4, 8))] |
| sr_sample_inverse_gamma | scalar | Draw k InverseGamma(shape, scale) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_inverse_gamma(2.0, 2.0, 10))] |
| sr_sample_laplace | scalar | Draw k Laplace(location, scale) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_laplace(0.0, 1.0, 10))] |
| sr_sample_levy | scalar | Draw k Levy(mu, c) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_levy(0.0, 1.0, 10))] |
| sr_sample_log_normal | scalar | Draw k LogNormal(location, scale) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_log_normal(0.0, 1.0, 10))] |
| sr_sample_multinomial | scalar | Draw k multinomial count vectors (UBIGINT LISTs summing to n) given category probabilities and the trial count | NULL | [SELECT len(sr_sample_multinomial([0.3, 0.7], 10, 4))] |
| sr_sample_multivariate_normal | scalar | Draw k MultivariateNormal samples (mean LIST, row-major flattened covariance LIST) as a LIST of point LISTs | NULL | [SELECT len(sr_sample_multivariate_normal([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 4))] |
| sr_sample_multivariate_students_t | scalar | Draw k multivariate Student's t samples (location LIST, row-major flattened scale LIST, degrees of freedom) as a LIST of point LISTs | NULL | [SELECT len(sr_sample_multivariate_students_t([0.0, 0.0], [1.0, 0.0, 0.0, 1.0], 3.0, 4))] |
| sr_sample_negative_binomial | scalar | Draw k NegativeBinomial(r, p) samples into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_negative_binomial(2.0, 0.5, 10))] |
| sr_sample_normal | scalar | Draw k Normal(mean, std_dev) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_normal(0.0, 1.0, 10))] |
| sr_sample_pareto | scalar | Draw k Pareto(scale, shape) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_pareto(1.0, 2.0, 10))] |
| sr_sample_poisson | scalar | Draw k Poisson(lambda) samples into a LIST(UBIGINT) | NULL | [SELECT len(sr_sample_poisson(3.0, 10))] |
| sr_sample_students_t | scalar | Draw k Student's t(location, scale, freedom) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_students_t(0.0, 1.0, 2.0, 10))] |
| sr_sample_triangular | scalar | Draw k Triangular(min, max, mode) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_triangular(0.0, 2.0, 1.0, 10))] |
| sr_sample_uniform | scalar | Draw k continuous Uniform(min, max) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_uniform(0.0, 1.0, 10))] |
| sr_sample_weibull | scalar | Draw k Weibull(shape, scale) samples into a LIST(DOUBLE) | NULL | [SELECT len(sr_sample_weibull(1.0, 1.0, 10))] |
| sr_skewness | aggregate | Sample skewness of a DOUBLE column (statrs' OnlineMoments<3>, m3/m2^1.5), NULL when fewer than two rows are non-NULL; constant columns give 0 | Fewer than two observations have no skewness; a zero-variance column is defined as 0, following statrs | [SELECT sr_skewness(x) FROM (VALUES (2.0), (4.0), (4.0), (4.0), (5.0), (5.0), (7.0), (9.0)) t(x)] |
| sr_skewtest | scalar | Skewness z-test of a LIST(DOUBLE) sample: LIST [z statistic, p-value]; same alternative and NaN-policy codes as sr_ttest_onesample | NULL | [SELECT sr_skewtest([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], 1.0, 1.0)] |
| sr_sqrt_2pi | scalar | The constant sqrt(2*PI), statrs' normalizing factor for the Gaussian density | NULL | [SELECT sr_sqrt_2pi()] |
| sr_std_dev | aggregate | Sample standard deviation of a DOUBLE column (Bessel-corrected), NULL when fewer than two rows are non-NULL | One value has no sample standard deviation; the result is NULL, not 0 | [SELECT sr_std_dev(x) FROM (VALUES (0.0), (3.0), (-2.0)) t(x)] |
| sr_students_t_cdf | scalar | Student's t cumulative distribution function P(X <= x) | NULL | [SELECT sr_students_t_cdf(1.0, 0.0, 1.0, 2.0)] |
| sr_students_t_entropy | scalar | Student's t distribution differential entropy | NULL | [SELECT sr_students_t_entropy(0.0, 1.0, 10.0)] |
| sr_students_t_ln_pdf | scalar | Student's t log-density at x | NULL | [SELECT sr_students_t_ln_pdf(1.0, 0.0, 1.0, 2.0)] |
| sr_students_t_max | scalar | Student's t distribution support maximum (positive infinity) | NULL | [SELECT sr_students_t_max(0.0, 1.0, 10.0)] |
| sr_students_t_mean | scalar | Student's t distribution mean | NULL | [SELECT sr_students_t_mean(0.0, 1.0, 2.0)] |
| sr_students_t_median | scalar | Student's t distribution median | NULL | [SELECT sr_students_t_median(0.0, 1.0, 10.0)] |
| sr_students_t_min | scalar | Student's t distribution support minimum (negative infinity) | NULL | [SELECT sr_students_t_min(0.0, 1.0, 10.0)] |
| sr_students_t_mode | scalar | Student's t distribution mode | NULL | [SELECT sr_students_t_mode(0.0, 1.0, 10.0)] |
| sr_students_t_pdf | scalar | Student's t probability density at x, given location, scale and degrees of freedom | NULL | [SELECT sr_students_t_pdf(1.0, 0.0, 1.0, 2.0)] |
| sr_students_t_quantile | scalar | Student's t quantile function: the x whose CDF equals p, for p in [0, 1] | statrs solves this one numerically (bisection), accuracy is lower than the closed forms | [SELECT sr_students_t_quantile(0.975, 0.0, 1.0, 10.0)] |
| sr_students_t_sf | scalar | Student's t survival function P(X > x) | NULL | [SELECT sr_students_t_sf(1.0, 0.0, 1.0, 2.0)] |
| sr_students_t_skewness | scalar | Student's t distribution skewness | NULL | [SELECT sr_students_t_skewness(0.0, 1.0, 10.0)] |
| sr_students_t_std_dev | scalar | Student's t distribution standard deviation | NULL | [SELECT sr_students_t_std_dev(0.0, 1.0, 10.0)] |
| sr_students_t_variance | scalar | Student's t distribution variance | NULL | [SELECT sr_students_t_variance(0.0, 1.0, 10.0)] |
| sr_triangular_cdf | scalar | Triangular cumulative distribution function P(X <= x) | NULL | [SELECT sr_triangular_cdf(1.0, 0.0, 2.0, 1.0)] |
| sr_triangular_entropy | scalar | Triangular distribution differential entropy | NULL | [SELECT sr_triangular_entropy(0.0, 2.0, 1.0)] |
| sr_triangular_ln_pdf | scalar | Triangular log-density at x | NULL | [SELECT sr_triangular_ln_pdf(1.0, 0.0, 2.0, 1.0)] |
| sr_triangular_max | scalar | Triangular distribution support maximum (max) | NULL | [SELECT sr_triangular_max(0.0, 2.0, 1.0)] |
| sr_triangular_mean | scalar | Triangular distribution mean | NULL | [SELECT sr_triangular_mean(0.0, 2.0, 1.0)] |
| sr_triangular_median | scalar | Triangular distribution median | NULL | [SELECT sr_triangular_median(0.0, 2.0, 1.0)] |
| sr_triangular_min | scalar | Triangular distribution support minimum (min) | NULL | [SELECT sr_triangular_min(0.0, 2.0, 1.0)] |
| sr_triangular_mode | scalar | Triangular distribution mode | NULL | [SELECT sr_triangular_mode(0.0, 2.0, 1.0)] |
| sr_triangular_pdf | scalar | Triangular probability density at x, given min, max and mode | NULL | [SELECT sr_triangular_pdf(1.0, 0.0, 2.0, 1.0)] |
| sr_triangular_quantile | scalar | Triangular quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_triangular_quantile(0.5, 0.0, 2.0, 1.0)] |
| sr_triangular_sf | scalar | Triangular survival function P(X > x) | NULL | [SELECT sr_triangular_sf(1.0, 0.0, 2.0, 1.0)] |
| sr_triangular_skewness | scalar | Triangular distribution skewness | NULL | [SELECT sr_triangular_skewness(0.0, 2.0, 1.0)] |
| sr_triangular_std_dev | scalar | Triangular distribution standard deviation | NULL | [SELECT sr_triangular_std_dev(0.0, 2.0, 1.0)] |
| sr_triangular_variance | scalar | Triangular distribution variance | NULL | [SELECT sr_triangular_variance(0.0, 2.0, 1.0)] |
| sr_ttest_onesample | scalar | One-sample t-test of a LIST(DOUBLE) sample against popmean: LIST [t statistic, p-value]; alternative 1 two-sided 2 less 3 greater, NaN policy 1 propagate 2 emit 3 error | NULL | [SELECT sr_ttest_onesample([1.0, 2.0, 3.0, 4.0], 2.5, 1.0, 1.0)] |
| sr_uniform_cdf | scalar | Continuous uniform cumulative distribution function P(X <= x) | NULL | [SELECT sr_uniform_cdf(0.5, 0.0, 1.0)] |
| sr_uniform_entropy | scalar | Continuous uniform distribution differential entropy | NULL | [SELECT sr_uniform_entropy(0.0, 1.0)] |
| sr_uniform_ln_pdf | scalar | Continuous uniform log-density at x | NULL | [SELECT sr_uniform_ln_pdf(0.5, 0.0, 1.0)] |
| sr_uniform_max | scalar | Continuous uniform distribution support maximum (max) | NULL | [SELECT sr_uniform_max(0.0, 1.0)] |
| sr_uniform_mean | scalar | Continuous uniform distribution mean | NULL | [SELECT sr_uniform_mean(0.0, 1.0)] |
| sr_uniform_median | scalar | Continuous uniform distribution median | NULL | [SELECT sr_uniform_median(0.0, 1.0)] |
| sr_uniform_min | scalar | Continuous uniform distribution support minimum (min) | NULL | [SELECT sr_uniform_min(0.0, 1.0)] |
| sr_uniform_mode | scalar | Continuous uniform distribution mode | NULL | [SELECT sr_uniform_mode(0.0, 1.0)] |
| sr_uniform_pdf | scalar | Continuous uniform probability density at x on [min, max] | NULL | [SELECT sr_uniform_pdf(0.5, 0.0, 1.0)] |
| sr_uniform_quantile | scalar | Continuous uniform quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_uniform_quantile(0.25, 0.0, 1.0)] |
| sr_uniform_sf | scalar | Continuous uniform survival function P(X > x) | NULL | [SELECT sr_uniform_sf(0.5, 0.0, 1.0)] |
| sr_uniform_skewness | scalar | Continuous uniform distribution skewness (always 0) | NULL | [SELECT sr_uniform_skewness(0.0, 1.0)] |
| sr_uniform_std_dev | scalar | Continuous uniform distribution standard deviation | NULL | [SELECT sr_uniform_std_dev(0.0, 1.0)] |
| sr_uniform_variance | scalar | Continuous uniform distribution variance | NULL | [SELECT sr_uniform_variance(0.0, 1.0)] |
| sr_upper_quartile | aggregate | Third quartile (upper hinge) of a DOUBLE column, NULL when no row is non-NULL | NULL | [SELECT sr_upper_quartile(x) FROM (VALUES (2.0), (1.0), (3.0), (4.0)) t(x)] |
| sr_variance | aggregate | Sample variance of a DOUBLE column (Bessel-corrected), NULL when fewer than two rows are non-NULL | One value has no sample variance; the result is NULL, not 0 | [SELECT sr_variance(x) FROM (VALUES (0.0), (3.0), (-2.0)) t(x)] |
| sr_weibull_cdf | scalar | Weibull cumulative distribution function P(X <= x) | NULL | [SELECT sr_weibull_cdf(1.0, 1.0, 1.0)] |
| sr_weibull_entropy | scalar | Weibull differential entropy, given shape k and scale lambda | NULL | [SELECT sr_weibull_entropy(1.0, 1.0)] |
| sr_weibull_ln_pdf | scalar | Weibull log-density at x | NULL | [SELECT sr_weibull_ln_pdf(1.0, 1.0, 1.0)] |
| sr_weibull_max | scalar | Weibull maximum of the support (positive infinity) | NULL | [SELECT sr_weibull_max(1.0, 1.0)] |
| sr_weibull_mean | scalar | Weibull mean, given shape k and scale lambda | NULL | [SELECT sr_weibull_mean(1.0, 1.0)] |
| sr_weibull_median | scalar | Weibull median, given shape k and scale lambda | NULL | [SELECT sr_weibull_median(1.0, 1.0)] |
| sr_weibull_min | scalar | Weibull minimum of the support (0) | NULL | [SELECT sr_weibull_min(1.0, 1.0)] |
| sr_weibull_mode | scalar | Weibull mode, given shape k and scale lambda | NULL | [SELECT sr_weibull_mode(2.0, 1.0)] |
| sr_weibull_pdf | scalar | Weibull probability density at x, given shape and scale | NULL | [SELECT sr_weibull_pdf(1.0, 1.0, 1.0)] |
| sr_weibull_quantile | scalar | Weibull quantile function: the x whose CDF equals p, for p in [0, 1] | NULL | [SELECT sr_weibull_quantile(0.5, 1.0, 1.0)] |
| sr_weibull_sf | scalar | Weibull survival function P(X > x) | NULL | [SELECT sr_weibull_sf(1.0, 1.0, 1.0)] |
| sr_weibull_skewness | scalar | Weibull skewness, given shape k and scale lambda | NULL | [SELECT sr_weibull_skewness(1.0, 1.0)] |
| sr_weibull_std_dev | scalar | Weibull standard deviation, given shape k and scale lambda | NULL | [SELECT sr_weibull_std_dev(1.0, 1.0)] |
| sr_weibull_variance | scalar | Weibull variance, given shape k and scale lambda | NULL | [SELECT sr_weibull_variance(1.0, 1.0)] |
Overloaded Functions
This extension does not add any function overloads.
Added Types
This extension does not add any types.
Added Settings
This extension does not add any settings.