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DuckDB Extensions All extensions Stochastic

Beta functions in the Stochastic DuckDB extension

Function category

Beta

21 functions

Beta distribution on [0,1] — shape parameters α, β. Common for Bayesian priors over probabilities and modeling proportions.

dist_beta_cdf

Scalar function Beta
Signature
dist_beta_cdf( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative distribution function (CDF) of the beta distribution. Returns the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_beta_cdf(2.0, 5.0, 0.5);

Output

dist_beta_cdf(2.0, 5.0, 0.5)
0.890625
Related functions

dist_beta_cdf_complement

Scalar function Beta
Signature
dist_beta_cdf_complement( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the complementary cumulative distribution function (1 - CDF) of the beta distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_beta_cdf_complement(2.0, 5.0, 0.5);

Output

dist_beta_cdf_complement(2.0, 5.0, 0.5)
0.109375
Related functions

dist_beta_chf

Scalar function Beta
Signature
dist_beta_chf( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the beta distribution.

1 Example 1 
SELECT dist_beta_chf(2.0, 5.0, 0.5);

Output

dist_beta_chf(2.0, 5.0, 0.5)
2.2129729343043585
Related functions

dist_beta_hazard

Scalar function Beta
Signature
dist_beta_hazard( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the beta distribution.

1 Example 1 
SELECT dist_beta_hazard(2.0, 5.0, 0.5);

Output

dist_beta_hazard(2.0, 5.0, 0.5)
8.571428571428571
Related functions

dist_beta_kurtosis

Scalar function Beta
Signature
dist_beta_kurtosis(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the beta distribution.

1 Example 1 
SELECT dist_beta_kurtosis(2.0, 5.0);

Output

dist_beta_kurtosis(2.0, 5.0)
2.88
Related functions

dist_beta_kurtosis_excess

Scalar function Beta
Signature
dist_beta_kurtosis_excess(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the beta distribution.

1 Example 1 
SELECT dist_beta_kurtosis_excess(2.0, 5.0);

Output

dist_beta_kurtosis_excess(2.0, 5.0)
-0.12
Related functions

dist_beta_log_cdf

Scalar function Beta
Signature
dist_beta_log_cdf( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the natural logarithm of the cumulative distribution function (CDF) of the beta distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_beta_log_cdf(2.0, 5.0, 0.5);

Output

dist_beta_log_cdf(2.0, 5.0, 0.5)
-0.1158318155251217
Related functions

dist_beta_log_cdf_complement

Scalar function Beta
Signature
dist_beta_log_cdf_complement( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the beta distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_beta_log_cdf_complement(2.0, 5.0, 0.5);

Output

dist_beta_log_cdf_complement(2.0, 5.0, 0.5)
-2.2129729343043585
Related functions

dist_beta_log_pdf

Scalar function Beta
Signature
dist_beta_log_pdf( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the natural logarithm of the probability density function (log-PDF) of the beta distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_beta_log_pdf(2.0, 5.0, 0.5);

Output

dist_beta_log_pdf(2.0, 5.0, 0.5)
-0.06453852113757129
Related functions

dist_beta_mean

Scalar function Beta
Signature
dist_beta_mean(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the mean (μ) of the beta distribution, which is the first moment.

1 Example 1 
SELECT dist_beta_mean(2.0, 5.0);

Output

dist_beta_mean(2.0, 5.0)
0.2857142857142857
Related functions

dist_beta_median

Scalar function Beta
Signature
dist_beta_median(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the median (50th percentile) of the beta distribution, which equals the mean.

1 Example 1 
SELECT dist_beta_median(2.0, 5.0);

Output

dist_beta_median(2.0, 5.0)
0.26444998329566005
Related functions

dist_beta_mode

Scalar function Beta
Signature
dist_beta_mode(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the mode (most likely value) of the beta distribution, which equals the mean.

1 Example 1 
SELECT dist_beta_mode(2.0, 5.0);

Output

dist_beta_mode(2.0, 5.0)
0.2
Related functions

dist_beta_pdf

Scalar function Beta
Signature
dist_beta_pdf( alpha: DOUBLE, beta: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the probability density function (PDF) of the beta distribution. Returns the probability densityat point x for a beta distribution with specified parameters.

1 Example 1 
SELECT dist_beta_pdf(2.0, 5.0, 0.5);

Output

dist_beta_pdf(2.0, 5.0, 0.5)
0.9374999999999999
Related functions

dist_beta_quantile

Scalar function Beta
Signature
dist_beta_quantile( alpha: DOUBLE, beta: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

Computes the quantile function (inverse CDF) of the beta distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

1 Example 1 
SELECT dist_beta_quantile(2.0, 5.0, 0.95);

Output

dist_beta_quantile(2.0, 5.0, 0.95)
0.5818034092520259
Related functions

dist_beta_quantile_complement

Scalar function Beta
Signature
dist_beta_quantile_complement( alpha: DOUBLE, beta: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

Computes the complementary quantile function of the beta distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.

1 Example 1 
SELECT dist_beta_quantile_complement(2.0, 5.0, 0.05);

Output

dist_beta_quantile_complement(2.0, 5.0, 0.05)
0.5818034092520259
Related functions

dist_beta_range

Scalar function Beta
Signature
dist_beta_range(alpha: DOUBLE, beta: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the range of the beta distribution.

1 Example 1 
SELECT dist_beta_range(2.0, 5.0);

Output

dist_beta_range(2.0, 5.0)
(0.0, 1.0)
Related functions

dist_beta_sample

Scalar function Beta
Signature
dist_beta_sample(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Generates random samples from the beta distribution with specified parameters.

1 Example 1 
SELECT dist_beta_sample(2.0, 5.0);

Output

dist_beta_sample(2.0, 5.0)
0.49894986644503236
Related functions

dist_beta_skewness

Scalar function Beta
Signature
dist_beta_skewness(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the skewness of the beta distribution.

1 Example 1 
SELECT dist_beta_skewness(2.0, 5.0);

Output

dist_beta_skewness(2.0, 5.0)
0.5962847939999439
Related functions

dist_beta_stddev

Scalar function Beta
Signature
dist_beta_stddev(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the standard deviation (σ) of the beta distribution.

1 Example 1 
SELECT dist_beta_stddev(2.0, 5.0);

Output

dist_beta_stddev(2.0, 5.0)
0.15971914124998499
Related functions

dist_beta_support

Scalar function Beta
Signature
dist_beta_support(alpha: DOUBLE, beta: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the support of the beta distribution.

1 Example 1 
SELECT dist_beta_support(2.0, 5.0);

Output

dist_beta_support(2.0, 5.0)
(0.0, 1.0)
Related functions

dist_beta_variance

Scalar function Beta
Signature
dist_beta_variance(alpha: DOUBLE, beta: DOUBLE) → DOUBLE
Arguments (Positional)
Argument alpha Type DOUBLE Mode Positional Description
Argument beta Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the beta distribution.

1 Example 1 
SELECT dist_beta_variance(2.0, 5.0);

Output

dist_beta_variance(2.0, 5.0)
0.025510204081632654
Related functions