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DuckDB Extensions All extensions Stochastic

Geometric functions in the Stochastic DuckDB extension

Function category

Geometric

21 functions

Geometric — number of failures before the first success in a Bernoulli trial sequence.

dist_geometric_cdf

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Returns the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_geometric_cdf(0.5, 2);

Output

dist_geometric_cdf(0.5, 2)
0.875
Related functions

dist_geometric_cdf_complement

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Returns the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_geometric_cdf_complement(0.5, 2);

Output

dist_geometric_cdf_complement(0.5, 2)
0.12500000000000003
Related functions

dist_geometric_chf

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution.

1 Example 1 
SELECT dist_geometric_chf(0.5, 2);

Output

dist_geometric_chf(0.5, 2)
2.0794415416798357
Related functions

dist_geometric_hazard

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution.

1 Example 1 
SELECT dist_geometric_hazard(0.5, 2);

Output

dist_geometric_hazard(0.5, 2)
0.9999999999999998
Related functions

dist_geometric_kurtosis

Scalar function Geometric
Signature
dist_geometric_kurtosis(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the geometric distribution.

1 Example 1 
SELECT dist_geometric_kurtosis(0.5);

Output

dist_geometric_kurtosis(0.5)
9.5
Related functions

dist_geometric_kurtosis_excess

Scalar function Geometric
Signature
dist_geometric_kurtosis_excess(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the geometric distribution.

1 Example 1 
SELECT dist_geometric_kurtosis_excess(0.5);

Output

dist_geometric_kurtosis_excess(0.5)
6.5
Related functions

dist_geometric_log_cdf

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_geometric_log_cdf(0.5, 2);

Output

dist_geometric_log_cdf(0.5, 2)
-0.13353139262452265
Related functions

dist_geometric_log_cdf_complement

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_geometric_log_cdf_complement(0.5, 2);

Output

dist_geometric_log_cdf_complement(0.5, 2)
-2.0794415416798357
Related functions

dist_geometric_log_pdf

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_geometric_log_pdf(0.5, 2);

Output

dist_geometric_log_pdf(0.5, 2)
-2.0794415416798357
Related functions

dist_geometric_mean

Scalar function Geometric
Signature
dist_geometric_mean(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_geometric_mean(0.5);

Output

dist_geometric_mean(0.5)
1.0
Related functions

dist_geometric_median

Scalar function Geometric
Signature
dist_geometric_median(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_geometric_median(0.5);

Output

dist_geometric_median(0.5)
0.0
Related functions

dist_geometric_mode

Scalar function Geometric
Signature
dist_geometric_mode(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_geometric_mode(0.5);

Output

dist_geometric_mode(0.5)
0.0
Related functions

dist_geometric_pdf

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Returns the probability densityat point x for a geometric distribution with specified parameters.

1 Example 1 
SELECT dist_geometric_pdf(0.5, 2);

Output

dist_geometric_pdf(0.5, 2)
0.125
Related functions

dist_geometric_quantile

Scalar function Geometric
Signature
dist_geometric_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 geometric distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.

1 Example 1 
SELECT dist_geometric_quantile(0.5, 0.95);

Output

dist_geometric_quantile(0.5, 0.95)
3.321928094887361
Related functions

dist_geometric_quantile_complement

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

1 Example 1 
SELECT dist_geometric_quantile_complement(0.5, 0.05);

Output

dist_geometric_quantile_complement(0.5, 0.05)
3.3219280948873626
Related functions

dist_geometric_range

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

Returns the range of the geometric distribution.

1 Example 1 
SELECT dist_geometric_range(0.5);

Output

dist_geometric_range(0.5)
(0.0, 1.7976931348623157e+308)
Related functions

dist_geometric_sample

Scalar function Geometric
Signature
dist_geometric_sample(p: DOUBLE) → BIGINT
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Generates random samples from the geometric distribution with specified parameters.

1 Example 1 
SELECT dist_geometric_sample(0.5);

Output

dist_geometric_sample(0.5)
3
Related functions

dist_geometric_skewness

Scalar function Geometric
Signature
dist_geometric_skewness(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the skewness of the geometric distribution.

1 Example 1 
SELECT dist_geometric_skewness(0.5);

Output

dist_geometric_skewness(0.5)
2.1213203435596424
Related functions

dist_geometric_stddev

Scalar function Geometric
Signature
dist_geometric_stddev(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_geometric_stddev(0.5);

Output

dist_geometric_stddev(0.5)
1.4142135623730951
Related functions

dist_geometric_support

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

Returns the support of the geometric distribution.

1 Example 1 
SELECT dist_geometric_support(0.5);

Output

dist_geometric_support(0.5)
(0.0, 1.7976931348623157e+308)
Related functions

dist_geometric_variance

Scalar function Geometric
Signature
dist_geometric_variance(p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument p Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the geometric distribution.

1 Example 1 
SELECT dist_geometric_variance(0.5);

Output

dist_geometric_variance(0.5)
2.0
Related functions