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DuckDB Extensions All extensions Stochastic

Poisson functions in the Stochastic DuckDB extension

Function category

Poisson

21 functions

Poisson — count of independent events in fixed interval at rate λ. Arrivals, defects, rare-event counts.

dist_poisson_cdf

Scalar function Poisson
Signature
dist_poisson_cdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_cdf(5.0, 3);

Output

dist_poisson_cdf(5.0, 3)
0.2650259152973617
Related functions

dist_poisson_cdf_complement

Scalar function Poisson
Signature
dist_poisson_cdf_complement(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_cdf_complement(5.0, 3);

Output

dist_poisson_cdf_complement(5.0, 3)
0.7349740847026383
Related functions

dist_poisson_chf

Scalar function Poisson
Signature
dist_poisson_chf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the poisson distribution.

1 Example 1 
SELECT dist_poisson_chf(5.0, 3);

Output

dist_poisson_chf(5.0, 3)
0.30792003929888545
Related functions

dist_poisson_hazard

Scalar function Poisson
Signature
dist_poisson_hazard(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the poisson distribution.

1 Example 1 
SELECT dist_poisson_hazard(5.0, 3);

Output

dist_poisson_hazard(5.0, 3)
0.1909916264205072
Related functions

dist_poisson_kurtosis

Scalar function Poisson
Signature
dist_poisson_kurtosis(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the poisson distribution.

1 Example 1 
SELECT dist_poisson_kurtosis(5.0);

Output

dist_poisson_kurtosis(5.0)
3.2
Related functions

dist_poisson_kurtosis_excess

Scalar function Poisson
Signature
dist_poisson_kurtosis_excess(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the poisson distribution.

1 Example 1 
SELECT dist_poisson_kurtosis_excess(5.0);

Output

dist_poisson_kurtosis_excess(5.0)
0.2
Related functions

dist_poisson_log_cdf

Scalar function Poisson
Signature
dist_poisson_log_cdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate 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 poisson distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_poisson_log_cdf(5.0, 3);

Output

dist_poisson_log_cdf(5.0, 3)
-1.327927664202445
Related functions

dist_poisson_log_cdf_complement

Scalar function Poisson
Signature
dist_poisson_log_cdf_complement(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate 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 poisson distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_poisson_log_cdf_complement(5.0, 3);

Output

dist_poisson_log_cdf_complement(5.0, 3)
-0.30792003929888545
Related functions

dist_poisson_log_pdf

Scalar function Poisson
Signature
dist_poisson_log_pdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate 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 poisson distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_poisson_log_pdf(5.0, 3);

Output

dist_poisson_log_pdf(5.0, 3)
-1.963445731925754
Related functions

dist_poisson_mean

Scalar function Poisson
Signature
dist_poisson_mean(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_mean(5.0);

Output

dist_poisson_mean(5.0)
5.0
Related functions

dist_poisson_median

Scalar function Poisson
Signature
dist_poisson_median(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_median(5.0);

Output

dist_poisson_median(5.0)
5.0
Related functions

dist_poisson_mode

Scalar function Poisson
Signature
dist_poisson_mode(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_mode(5.0);

Output

dist_poisson_mode(5.0)
5.0
Related functions

dist_poisson_pdf

Scalar function Poisson
Signature
dist_poisson_pdf(rate: DOUBLE, x: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_pdf(5.0, 3);

Output

dist_poisson_pdf(5.0, 3)
0.1403738958142805
Related functions

dist_poisson_quantile

Scalar function Poisson
Signature
dist_poisson_quantile(rate: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_quantile(5.0, 0.95);

Output

dist_poisson_quantile(5.0, 0.95)
9.0
Related functions

dist_poisson_quantile_complement

Scalar function Poisson
Signature
dist_poisson_quantile_complement(rate: DOUBLE, p: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_quantile_complement(5.0, 0.05);

Output

dist_poisson_quantile_complement(5.0, 0.05)
9.0
Related functions

dist_poisson_range

Scalar function Poisson
Signature
dist_poisson_range(rate: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the range of the poisson distribution.

1 Example 1 
SELECT dist_poisson_range(5.0);

Output

dist_poisson_range(5.0)
(0.0, 1.7976931348623157e+308)
Related functions

dist_poisson_sample

Scalar function Poisson
Signature
dist_poisson_sample(rate: DOUBLE) → BIGINT
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Generates random samples from the poisson distribution with specified parameters.

1 Example 1 
SELECT dist_poisson_sample(5.0);

Output

dist_poisson_sample(5.0)
5
Related functions

dist_poisson_skewness

Scalar function Poisson
Signature
dist_poisson_skewness(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the skewness of the poisson distribution.

1 Example 1 
SELECT dist_poisson_skewness(5.0);

Output

dist_poisson_skewness(5.0)
0.4472135954999579
Related functions

dist_poisson_stddev

Scalar function Poisson
Signature
dist_poisson_stddev(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_poisson_stddev(5.0);

Output

dist_poisson_stddev(5.0)
2.23606797749979
Related functions

dist_poisson_support

Scalar function Poisson
Signature
dist_poisson_support(rate: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the support of the poisson distribution.

1 Example 1 
SELECT dist_poisson_support(5.0);

Output

dist_poisson_support(5.0)
(0.0, 1.7976931348623157e+308)
Related functions

dist_poisson_variance

Scalar function Poisson
Signature
dist_poisson_variance(rate: DOUBLE) → DOUBLE
Arguments (Positional)
Argument rate Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the poisson distribution.

1 Example 1 
SELECT dist_poisson_variance(5.0);

Output

dist_poisson_variance(5.0)
5.0
Related functions