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DuckDB Extensions All extensions Stochastic

Binomial functions in the Stochastic DuckDB extension

Function category

Binomial

19 functions

Binomial — number of successes in n independent Bernoulli trials at probability p.

dist_binomial_cdf

Scalar function Binomial
Signature
dist_binomial_cdf( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution. Returns the probability that a random variable X is less than or equal to x.

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

Output

dist_binomial_cdf(10, 0.5, 5)
0.623046875
Related functions

dist_binomial_cdf_complement

Scalar function Binomial
Signature
dist_binomial_cdf_complement( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution. Returns the probability that X > x, equivalent to the survival function.

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

Output

dist_binomial_cdf_complement(10, 0.5, 5)
0.376953125
Related functions

dist_binomial_chf

Scalar function Binomial
Signature
dist_binomial_chf( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution.

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

Output

dist_binomial_chf(10, 0.5, 5)
0.9756344361346222
Related functions

dist_binomial_hazard

Scalar function Binomial
Signature
dist_binomial_hazard( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution.

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

Output

dist_binomial_hazard(10, 0.5, 5)
0.652849740932643
Related functions

dist_binomial_kurtosis

Scalar function Binomial
Signature
dist_binomial_kurtosis(trials: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the binomial distribution.

1 Example 1 
SELECT dist_binomial_kurtosis(10, 0.5);

Output

dist_binomial_kurtosis(10, 0.5)
2.8
Related functions

dist_binomial_kurtosis_excess

Scalar function Binomial
Signature
dist_binomial_kurtosis_excess(trials: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the binomial distribution.

1 Example 1 
SELECT dist_binomial_kurtosis_excess(10, 0.5);

Output

dist_binomial_kurtosis_excess(10, 0.5)
-0.2
Related functions

dist_binomial_log_cdf

Scalar function Binomial
Signature
dist_binomial_log_cdf( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 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_binomial_log_cdf(10, 0.5, 5);

Output

dist_binomial_log_cdf(10, 0.5, 5)
-0.4731335222546632
Related functions

dist_binomial_log_cdf_complement

Scalar function Binomial
Signature
dist_binomial_log_cdf_complement( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

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

Output

dist_binomial_log_cdf_complement(10, 0.5, 5)
-0.9756344361346222
Related functions

dist_binomial_log_pdf

Scalar function Binomial
Signature
dist_binomial_log_pdf( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution. Useful for numerical stability when dealing with very small probabilities.

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

Output

dist_binomial_log_pdf(10, 0.5, 5)
-1.402042718088029
Related functions

dist_binomial_median

Scalar function Binomial
Signature
dist_binomial_median(trials: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_binomial_median(10, 0.5);

Output

dist_binomial_median(10, 0.5)
5.0
Related functions

dist_binomial_mode

Scalar function Binomial
Signature
dist_binomial_mode(trials: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_binomial_mode(10, 0.5);

Output

dist_binomial_mode(10, 0.5)
5.0
Related functions

dist_binomial_pdf

Scalar function Binomial
Signature
dist_binomial_pdf( trials: BIGINT, prob: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument trials 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 binomial distribution. Returns the probability densityat point x for a binomial distribution with specified parameters.

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

Output

dist_binomial_pdf(10, 0.5, 5)
0.2460937500000002
Related functions

dist_binomial_quantile

Scalar function Binomial
Signature
dist_binomial_quantile( trials: BIGINT, prob: DOUBLE, p: DOUBLE ) → BIGINT
Arguments (Positional)
Argument trials 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 binomial distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

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

Output

dist_binomial_quantile(10, 0.5, 0.95)
8
Related functions

dist_binomial_quantile_complement

Scalar function Binomial
Signature
dist_binomial_quantile_complement( trials: BIGINT, prob: DOUBLE, p: DOUBLE ) → BIGINT
Arguments (Positional)
Argument trials 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 binomial distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.

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

Output

dist_binomial_quantile_complement(10, 0.5, 0.05)
8
Related functions

dist_binomial_range

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

Returns the range of the binomial distribution.

1 Example 1 
SELECT dist_binomial_range(10, 0.5);

Output

dist_binomial_range(10, 0.5)
(0.0, 10.0)
Related functions

dist_binomial_sample

Scalar function Binomial
Signature
dist_binomial_sample(trials: BIGINT, prob: DOUBLE) → BIGINT
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Generates random samples from the binomial distribution with specified parameters.

1 Example 1 
SELECT dist_binomial_sample(10, 0.5);

Output

dist_binomial_sample(10, 0.5)
2
Related functions

dist_binomial_skewness

Scalar function Binomial
Signature
dist_binomial_skewness(trials: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the skewness of the binomial distribution.

1 Example 1 
SELECT dist_binomial_skewness(10, 0.5);

Output

dist_binomial_skewness(10, 0.5)
0.0
Related functions

dist_binomial_support

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

Returns the support of the binomial distribution.

1 Example 1 
SELECT dist_binomial_support(10, 0.5);

Output

dist_binomial_support(10, 0.5)
(0.0, 10.0)
Related functions

dist_binomial_variance

Scalar function Binomial
Signature
dist_binomial_variance(trials: BIGINT, prob: DOUBLE) → DOUBLE
Arguments (Positional)
Argument trials Type BIGINT Mode Positional Description
Argument prob Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the binomial distribution.

1 Example 1 
SELECT dist_binomial_variance(10, 0.5);

Output

dist_binomial_variance(10, 0.5)
2.5
Related functions