Skip to content
DuckDB Extensions All extensions Stochastic

Negative Binomial functions in the Stochastic DuckDB extension

Function category

Negative Binomial

19 functions

Negative Binomial — number of failures before r successes. Used for over-dispersed count data.

dist_negative_binomial_cdf

Scalar function Negative Binomial
Signature
dist_negative_binomial_cdf( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_cdf(10, 0.5, 5);

Output

dist_negative_binomial_cdf(10, 0.5, 5)
0.15087890624999997
Related functions

dist_negative_binomial_cdf_complement

Scalar function Negative Binomial
Signature
dist_negative_binomial_cdf_complement( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_cdf_complement(10, 0.5, 5);

Output

dist_negative_binomial_cdf_complement(10, 0.5, 5)
0.84912109375
Related functions

dist_negative_binomial_chf

Scalar function Negative Binomial
Signature
dist_negative_binomial_chf( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_chf(10, 0.5, 5);

Output

dist_negative_binomial_chf(10, 0.5, 5)
0.16355347180511537
Related functions

dist_negative_binomial_hazard

Scalar function Negative Binomial
Signature
dist_negative_binomial_hazard( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_hazard(10, 0.5, 5);

Output

dist_negative_binomial_hazard(10, 0.5, 5)
0.07195227142035647
Related functions

dist_negative_binomial_kurtosis

Scalar function Negative Binomial
Signature
dist_negative_binomial_kurtosis(successes: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_kurtosis(10, 0.5);

Output

dist_negative_binomial_kurtosis(10, 0.5)
3.65
Related functions

dist_negative_binomial_kurtosis_excess

Scalar function Negative Binomial
Signature
dist_negative_binomial_kurtosis_excess(successes: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_kurtosis_excess(10, 0.5);

Output

dist_negative_binomial_kurtosis_excess(10, 0.5)
0.65
Related functions

dist_negative_binomial_log_cdf

Scalar function Negative Binomial
Signature
dist_negative_binomial_log_cdf( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob 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 negative_binomial distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_negative_binomial_log_cdf(10, 0.5, 5);

Output

dist_negative_binomial_log_cdf(10, 0.5, 5)
-1.891277709261653
Related functions

dist_negative_binomial_log_cdf_complement

Scalar function Negative Binomial
Signature
dist_negative_binomial_log_cdf_complement( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob 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 negative_binomial distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_negative_binomial_log_cdf_complement(10, 0.5, 5);

Output

dist_negative_binomial_log_cdf_complement(10, 0.5, 5)
-0.16355347180511537
Related functions

dist_negative_binomial_log_pdf

Scalar function Negative Binomial
Signature
dist_negative_binomial_log_pdf( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob 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 negative_binomial distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_negative_binomial_log_pdf(10, 0.5, 5);

Output

dist_negative_binomial_log_pdf(10, 0.5, 5)
-2.7953057485240147
Related functions

dist_negative_binomial_median

Scalar function Negative Binomial
Signature
dist_negative_binomial_median(successes: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_median(10, 0.5);

Output

dist_negative_binomial_median(10, 0.5)
9.0
Related functions

dist_negative_binomial_mode

Scalar function Negative Binomial
Signature
dist_negative_binomial_mode(successes: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_mode(10, 0.5);

Output

dist_negative_binomial_mode(10, 0.5)
9.0
Related functions

dist_negative_binomial_pdf

Scalar function Negative Binomial
Signature
dist_negative_binomial_pdf( successes: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_pdf(10, 0.5, 5);

Output

dist_negative_binomial_pdf(10, 0.5, 5)
0.06109619140624995
Related functions

dist_negative_binomial_quantile

Scalar function Negative Binomial
Signature
dist_negative_binomial_quantile( successes: BIGINT, prob: DOUBLE, p: DOUBLE ) → BIGINT
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_quantile(10, 0.5, 0.95);

Output

dist_negative_binomial_quantile(10, 0.5, 0.95)
18
Related functions

dist_negative_binomial_quantile_complement

Scalar function Negative Binomial
Signature
dist_negative_binomial_quantile_complement( successes: BIGINT, prob: DOUBLE, p: DOUBLE ) → BIGINT
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_negative_binomial_quantile_complement(10, 0.5, 0.05);

Output

dist_negative_binomial_quantile_complement(10, 0.5, 0.05)
18
Related functions

dist_negative_binomial_range

Scalar function Negative Binomial
Signature
dist_negative_binomial_range(successes: BIGINT, prob: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the range of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_range(10, 0.5);

Output

dist_negative_binomial_range(10, 0.5)
(0.0, 1.7976931348623157e+308)
Related functions

dist_negative_binomial_sample

Scalar function Negative Binomial
Signature
dist_negative_binomial_sample(successes: BIGINT, prob: DOUBLE) → BIGINT
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Generates random samples from the negative_binomial distribution with specified parameters.

1 Example 1 
SELECT dist_negative_binomial_sample(10, 0.5);

Output

dist_negative_binomial_sample(10, 0.5)
7
Related functions

dist_negative_binomial_skewness

Scalar function Negative Binomial
Signature
dist_negative_binomial_skewness(successes: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the skewness of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_skewness(10, 0.5);

Output

dist_negative_binomial_skewness(10, 0.5)
0.6708203932499369
Related functions

dist_negative_binomial_support

Scalar function Negative Binomial
Signature
dist_negative_binomial_support(successes: BIGINT, prob: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the support of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_support(10, 0.5);

Output

dist_negative_binomial_support(10, 0.5)
(0.0, 1.7976931348623157e+308)
Related functions

dist_negative_binomial_variance

Scalar function Negative Binomial
Signature
dist_negative_binomial_variance(successes: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument successes Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the negative_binomial distribution.

1 Example 1 
SELECT dist_negative_binomial_variance(10, 0.5);

Output

dist_negative_binomial_variance(10, 0.5)
20.0
Related functions