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DuckDB Extensions All extensions Stochastic

Pareto functions in the Stochastic DuckDB extension

Function category

Pareto

21 functions

Pareto distribution — power-law tail with scale and shape. Wealth, file sizes, internet traffic; the 80/20 rule.

dist_pareto_cdf

Scalar function Pareto
Signature
dist_pareto_cdf( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_cdf(3.0, 1.0, 1.5);

Output

dist_pareto_cdf(3.0, 1.0, 1.5)
0.0
Related functions

dist_pareto_cdf_complement

Scalar function Pareto
Signature
dist_pareto_cdf_complement( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_cdf_complement(3.0, 1.0, 1.5);

Output

dist_pareto_cdf_complement(3.0, 1.0, 1.5)
1.0
Related functions

dist_pareto_chf

Scalar function Pareto
Signature
dist_pareto_chf( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the cumulative hazard function of the pareto distribution.

1 Example 1 
SELECT dist_pareto_chf(3.0, 1.0, 1.5);

Output

dist_pareto_chf(3.0, 1.0, 1.5)
-0.0
Related functions

dist_pareto_hazard

Scalar function Pareto
Signature
dist_pareto_hazard( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Computes the hazard function of the pareto distribution.

1 Example 1 
SELECT dist_pareto_hazard(3.0, 1.0, 1.5);

Output

dist_pareto_hazard(3.0, 1.0, 1.5)
0.0
Related functions

dist_pareto_kurtosis

Scalar function Pareto
Signature
dist_pareto_kurtosis(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Returns the kurtosis of the pareto distribution.

1 Kurtosis with scale 1 and shape 5 
SELECT dist_pareto_kurtosis(1.0, 5.0);
Related functions

dist_pareto_kurtosis_excess

Scalar function Pareto
Signature
dist_pareto_kurtosis_excess(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Returns the excess kurtosis of the pareto distribution.

1 Excess kurtosis with scale 1 and shape 5 
SELECT dist_pareto_kurtosis_excess(1.0, 5.0);
Related functions

dist_pareto_log_cdf

Scalar function Pareto
Signature
dist_pareto_log_cdf( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum 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 pareto distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.

1 Example 1 
SELECT dist_pareto_log_cdf(3.0, 1.0, 1.5);

Output

dist_pareto_log_cdf(3.0, 1.0, 1.5)
-inf
Related functions

dist_pareto_log_cdf_complement

Scalar function Pareto
Signature
dist_pareto_log_cdf_complement( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum 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 pareto distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.

1 Example 1 
SELECT dist_pareto_log_cdf_complement(3.0, 1.0, 1.5);

Output

dist_pareto_log_cdf_complement(3.0, 1.0, 1.5)
0.0
Related functions

dist_pareto_log_pdf

Scalar function Pareto
Signature
dist_pareto_log_pdf( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum 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 pareto distribution. Useful for numerical stability when dealing with very small probabilities.

1 Example 1 
SELECT dist_pareto_log_pdf(3.0, 1.0, 1.5);

Output

dist_pareto_log_pdf(3.0, 1.0, 1.5)
-inf
Related functions

dist_pareto_mean

Scalar function Pareto
Signature
dist_pareto_mean(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_mean(3.0, 1.0);

Output

dist_pareto_mean(3.0, 1.0)
1.7976931348623157e+308
Related functions

dist_pareto_median

Scalar function Pareto
Signature
dist_pareto_median(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_median(3.0, 1.0);

Output

dist_pareto_median(3.0, 1.0)
6.0
Related functions

dist_pareto_mode

Scalar function Pareto
Signature
dist_pareto_mode(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_mode(3.0, 1.0);

Output

dist_pareto_mode(3.0, 1.0)
3.0
Related functions

dist_pareto_pdf

Scalar function Pareto
Signature
dist_pareto_pdf( shape: DOUBLE, minimum: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_pdf(3.0, 1.0, 1.5);

Output

dist_pareto_pdf(3.0, 1.0, 1.5)
0.0
Related functions

dist_pareto_quantile

Scalar function Pareto
Signature
dist_pareto_quantile( shape: DOUBLE, minimum: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_quantile(3.0, 1.0, 0.95);

Output

dist_pareto_quantile(3.0, 1.0, 0.95)
59.99999999999995
Related functions

dist_pareto_quantile_complement

Scalar function Pareto
Signature
dist_pareto_quantile_complement( shape: DOUBLE, minimum: DOUBLE, p: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Argument p Type DOUBLE Mode Positional Description
Description

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

1 Example 1 
SELECT dist_pareto_quantile_complement(3.0, 1.0, 0.05);

Output

dist_pareto_quantile_complement(3.0, 1.0, 0.05)
60.0
Related functions

dist_pareto_range

Scalar function Pareto
Signature
dist_pareto_range(shape: DOUBLE, minimum: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Returns the range of the pareto distribution.

1 Example 1 
SELECT dist_pareto_range(3.0, 1.0);

Output

dist_pareto_range(3.0, 1.0)
(0.0, 1.7976931348623157e+308)
Related functions

dist_pareto_sample

Scalar function Pareto
Signature
dist_pareto_sample(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Generates random samples from the pareto distribution with specified parameters.

1 Example 1 
SELECT dist_pareto_sample(3.0, 1.0);

Output

dist_pareto_sample(3.0, 1.0)
3.3830474100303447
Related functions

dist_pareto_skewness

Scalar function Pareto
Signature
dist_pareto_skewness(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Returns the skewness of the pareto distribution.

1 Skewness with scale 1 and shape 5 
SELECT dist_pareto_skewness(1.0, 5.0);
Related functions

dist_pareto_stddev

Scalar function Pareto
Signature
dist_pareto_stddev(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

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

1 Standard deviation with scale 1 and shape 5 
SELECT dist_pareto_stddev(1.0, 5.0);
Related functions

dist_pareto_support

Scalar function Pareto
Signature
dist_pareto_support(shape: DOUBLE, minimum: DOUBLE) → DOUBLE[2]
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Returns the support of the pareto distribution.

1 Example 1 
SELECT dist_pareto_support(3.0, 1.0);

Output

dist_pareto_support(3.0, 1.0)
(3.0, 1.7976931348623157e+308)
Related functions

dist_pareto_variance

Scalar function Pareto
Signature
dist_pareto_variance(shape: DOUBLE, minimum: DOUBLE) → DOUBLE
Arguments (Positional)
Argument shape Type DOUBLE Mode Positional Description
Argument minimum Type DOUBLE Mode Positional Description
Description

Returns the variance (σ²) of the pareto distribution.

1 Variance with scale 1 and shape 5 
SELECT dist_pareto_variance(1.0, 5.0);
Related functions