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DuckDB Extensions All extensions Stochastic

Bernoulli functions in the Stochastic DuckDB extension

Function category

Bernoulli

21 functions

Bernoulli — single yes/no trial with success probability p. Foundation of every binary outcome model.

dist_bernoulli_cdf

Scalar function Bernoulli
Signature
dist_bernoulli_cdf(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_cdf(0.5, 0);

Output

dist_bernoulli_cdf(0.5, 0)
0.5
Related functions

dist_bernoulli_cdf_complement

Scalar function Bernoulli
Signature
dist_bernoulli_cdf_complement(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_cdf_complement(0.5, 0);

Output

dist_bernoulli_cdf_complement(0.5, 0)
0.5
Related functions

dist_bernoulli_chf

Scalar function Bernoulli
Signature
dist_bernoulli_chf(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_chf(0.5, 0);

Output

dist_bernoulli_chf(0.5, 0)
0.6931471805599453
Related functions

dist_bernoulli_hazard

Scalar function Bernoulli
Signature
dist_bernoulli_hazard(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_hazard(0.5, 0);

Output

dist_bernoulli_hazard(0.5, 0)
1.0
Related functions

dist_bernoulli_kurtosis

Scalar function Bernoulli
Signature
dist_bernoulli_kurtosis(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_kurtosis(0.5);

Output

dist_bernoulli_kurtosis(0.5)
1.0
Related functions

dist_bernoulli_kurtosis_excess

Scalar function Bernoulli
Signature
dist_bernoulli_kurtosis_excess(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_kurtosis_excess(0.5);

Output

dist_bernoulli_kurtosis_excess(0.5)
-2.0
Related functions

dist_bernoulli_log_cdf

Scalar function Bernoulli
Signature
dist_bernoulli_log_cdf(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p 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 bernoulli distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_bernoulli_log_cdf(0.5, 0);

Output

dist_bernoulli_log_cdf(0.5, 0)
-0.6931471805599453
Related functions

dist_bernoulli_log_cdf_complement

Scalar function Bernoulli
Signature
dist_bernoulli_log_cdf_complement(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p 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 bernoulli distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_bernoulli_log_cdf_complement(0.5, 0);

Output

dist_bernoulli_log_cdf_complement(0.5, 0)
-0.6931471805599453
Related functions

dist_bernoulli_log_pdf

Scalar function Bernoulli
Signature
dist_bernoulli_log_pdf(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p 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 bernoulli distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_bernoulli_log_pdf(0.5, 1);

Output

dist_bernoulli_log_pdf(0.5, 1)
-0.6931471805599453
Related functions

dist_bernoulli_mean

Scalar function Bernoulli
Signature
dist_bernoulli_mean(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_mean(0.5);

Output

dist_bernoulli_mean(0.5)
0.5
Related functions

dist_bernoulli_median

Scalar function Bernoulli
Signature
dist_bernoulli_median(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_median(0.5);

Output

dist_bernoulli_median(0.5)
0.0
Related functions

dist_bernoulli_mode

Scalar function Bernoulli
Signature
dist_bernoulli_mode(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_mode(0.5);

Output

dist_bernoulli_mode(0.5)
0.0
Related functions

dist_bernoulli_pdf

Scalar function Bernoulli
Signature
dist_bernoulli_pdf(p: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_pdf(0.5, 1);

Output

dist_bernoulli_pdf(0.5, 1)
0.5
Related functions

dist_bernoulli_quantile

Scalar function Bernoulli
Signature
dist_bernoulli_quantile(p: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_quantile(0.5, 0.95);

Output

dist_bernoulli_quantile(0.5, 0.95)
1.0
Related functions

dist_bernoulli_quantile_complement

Scalar function Bernoulli
Signature
dist_bernoulli_quantile_complement(p: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_quantile_complement(0.5, 0.05);

Output

dist_bernoulli_quantile_complement(0.5, 0.05)
1.0
Related functions

dist_bernoulli_range

Scalar function Bernoulli
Signature
dist_bernoulli_range(p: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the range of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_range(0.5);

Output

dist_bernoulli_range(0.5)
(0.0, 1.0)
Related functions

dist_bernoulli_sample

Scalar function Bernoulli
Signature
dist_bernoulli_sample(p: DOUBLE) → BOOLEAN
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Generates random samples from the bernoulli distribution with specified parameters.

1 Example 1 
SELECT dist_bernoulli_sample(0.5);

Output

dist_bernoulli_sample(0.5)
true
Related functions

dist_bernoulli_skewness

Scalar function Bernoulli
Signature
dist_bernoulli_skewness(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the skewness of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_skewness(0.5);

Output

dist_bernoulli_skewness(0.5)
0.0
Related functions

dist_bernoulli_stddev

Scalar function Bernoulli
Signature
dist_bernoulli_stddev(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_bernoulli_stddev(0.5);

Output

dist_bernoulli_stddev(0.5)
0.5
Related functions

dist_bernoulli_support

Scalar function Bernoulli
Signature
dist_bernoulli_support(p: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the support of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_support(0.5);

Output

dist_bernoulli_support(0.5)
(0.0, 1.0)
Related functions

dist_bernoulli_variance

Scalar function Bernoulli
Signature
dist_bernoulli_variance(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the bernoulli distribution.

1 Example 1 
SELECT dist_bernoulli_variance(0.5);

Output

dist_bernoulli_variance(0.5)
0.25
Related functions