Skip to content
DuckDB Extensions All extensions Stochastic

Gamma functions in the Stochastic DuckDB extension

Function category

Gamma

21 functions

Gamma distribution — shape/scale family. Waiting times for k events at constant rate; flexible right-skewed prior.

dist_gamma_cdf

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_gamma_cdf(2.0, 1.0, 1.5);

Output

dist_gamma_cdf(2.0, 1.0, 1.5)
0.44217459962892547
Related functions

dist_gamma_cdf_complement

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_gamma_cdf_complement(2.0, 1.0, 1.5);

Output

dist_gamma_cdf_complement(2.0, 1.0, 1.5)
0.5578254003710745
Related functions

dist_gamma_chf

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_chf(2.0, 1.0, 1.5);

Output

dist_gamma_chf(2.0, 1.0, 1.5)
0.583709268125845
Related functions

dist_gamma_hazard

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_hazard(2.0, 1.0, 1.5);

Output

dist_gamma_hazard(2.0, 1.0, 1.5)
0.6
Related functions

dist_gamma_kurtosis

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_kurtosis(2.0, 1.0);

Output

dist_gamma_kurtosis(2.0, 1.0)
6.0
Related functions

dist_gamma_kurtosis_excess

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_kurtosis_excess(2.0, 1.0);

Output

dist_gamma_kurtosis_excess(2.0, 1.0)
3.0
Related functions

dist_gamma_log_cdf

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_gamma_log_cdf(2.0, 1.0, 1.5);

Output

dist_gamma_log_cdf(2.0, 1.0, 1.5)
-0.8160504531201044
Related functions

dist_gamma_log_cdf_complement

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_gamma_log_cdf_complement(2.0, 1.0, 1.5);

Output

dist_gamma_log_cdf_complement(2.0, 1.0, 1.5)
-0.583709268125845
Related functions

dist_gamma_log_pdf

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_gamma_log_pdf(2.0, 1.0, 1.5);

Output

dist_gamma_log_pdf(2.0, 1.0, 1.5)
-1.0945348918918356
Related functions

dist_gamma_mean

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution, which is the first moment.

1 Example 1 
SELECT dist_gamma_mean(2.0, 1.0);

Output

dist_gamma_mean(2.0, 1.0)
2.0
Related functions

dist_gamma_median

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution, which equals the mean.

1 Example 1 
SELECT dist_gamma_median(2.0, 1.0);

Output

dist_gamma_median(2.0, 1.0)
1.6783469900166605
Related functions

dist_gamma_mode

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution, which equals the mean.

1 Example 1 
SELECT dist_gamma_mode(2.0, 1.0);

Output

dist_gamma_mode(2.0, 1.0)
1.0
Related functions

dist_gamma_pdf

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the probability densityat point x for a gamma distribution with specified parameters.

1 Example 1 
SELECT dist_gamma_pdf(2.0, 1.0, 1.5);

Output

dist_gamma_pdf(2.0, 1.0, 1.5)
0.3346952402226447
Related functions

dist_gamma_quantile

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

1 Example 1 
SELECT dist_gamma_quantile(2.0, 1.0, 0.95);

Output

dist_gamma_quantile(2.0, 1.0, 0.95)
4.743864518390577
Related functions

dist_gamma_quantile_complement

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.

1 Example 1 
SELECT dist_gamma_quantile_complement(2.0, 1.0, 0.05);

Output

dist_gamma_quantile_complement(2.0, 1.0, 0.05)
4.743864518390578
Related functions

dist_gamma_range

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_range(2.0, 1.0);

Output

dist_gamma_range(2.0, 1.0)
(0.0, 1.7976931348623157e+308)
Related functions

dist_gamma_sample

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution with specified parameters.

1 Example 1 
SELECT dist_gamma_sample(2.0, 1.0);

Output

dist_gamma_sample(2.0, 1.0)
1.036968725054842
Related functions

dist_gamma_skewness

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_skewness(2.0, 1.0);

Output

dist_gamma_skewness(2.0, 1.0)
1.414213562373095
Related functions

dist_gamma_stddev

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_stddev(2.0, 1.0);

Output

dist_gamma_stddev(2.0, 1.0)
1.4142135623730951
Related functions

dist_gamma_support

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_support(2.0, 1.0);

Output

dist_gamma_support(2.0, 1.0)
(2.2250738585072014e-308, 1.7976931348623157e+308)
Related functions

dist_gamma_variance

Scalar function Gamma
Signature
dist_gamma_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 gamma distribution.

1 Example 1 
SELECT dist_gamma_variance(2.0, 1.0);

Output

dist_gamma_variance(2.0, 1.0)
2.0
Related functions