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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( scale: DOUBLE, shape: DOUBLE, x: DOUBLE ) → DOUBLE
Arguments (Positional)
Argument scale Type DOUBLE Mode Positional Description
Argument shape Type DOUBLE Mode Positional Description
Argument x Type DOUBLE Mode Positional Description
Description

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_cdf(1.0, 3.0, 1.5);

Output

dist_pareto_cdf(1.0, 3.0, 1.5)
0.7037037037037037
Related functions

dist_pareto_cdf_complement

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_cdf_complement(1.0, 3.0, 1.5);

Output

dist_pareto_cdf_complement(1.0, 3.0, 1.5)
0.2962962962962962
Related functions

dist_pareto_chf

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_chf(1.0, 3.0, 1.5);

Output

dist_pareto_chf(1.0, 3.0, 1.5)
1.2163953243244934
Related functions

dist_pareto_hazard

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_hazard(1.0, 3.0, 1.5);

Output

dist_pareto_hazard(1.0, 3.0, 1.5)
2.0000000000000004
Related functions

dist_pareto_kurtosis

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_kurtosis(1.0, 5.0);

Output

dist_pareto_kurtosis(1.0, 5.0)
73.8
Related functions

dist_pareto_kurtosis_excess

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_kurtosis_excess(1.0, 5.0);

Output

dist_pareto_kurtosis_excess(1.0, 5.0)
70.8
Related functions

dist_pareto_log_cdf

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_log_cdf(1.0, 3.0, 1.5);

Output

dist_pareto_log_cdf(1.0, 3.0, 1.5)
-0.35139788683788853
Related functions

dist_pareto_log_cdf_complement

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_log_cdf_complement(1.0, 3.0, 1.5);

Output

dist_pareto_log_cdf_complement(1.0, 3.0, 1.5)
-1.2163953243244934
Related functions

dist_pareto_log_pdf

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_log_pdf(1.0, 3.0, 1.5);

Output

dist_pareto_log_pdf(1.0, 3.0, 1.5)
-0.5232481437645479
Related functions

dist_pareto_mean

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_mean(1.0, 3.0);

Output

dist_pareto_mean(1.0, 3.0)
1.5
Related functions

dist_pareto_median

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_median(1.0, 3.0);

Output

dist_pareto_median(1.0, 3.0)
1.2599210498948732
Related functions

dist_pareto_mode

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_mode(1.0, 3.0);

Output

dist_pareto_mode(1.0, 3.0)
1.0
Related functions

dist_pareto_pdf

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_pdf(1.0, 3.0, 1.5);

Output

dist_pareto_pdf(1.0, 3.0, 1.5)
0.5925925925925926
Related functions

dist_pareto_quantile

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_quantile(1.0, 3.0, 0.95);

Output

dist_pareto_quantile(1.0, 3.0, 0.95)
2.714417616594906
Related functions

dist_pareto_quantile_complement

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_quantile_complement(1.0, 3.0, 0.05);

Output

dist_pareto_quantile_complement(1.0, 3.0, 0.05)
2.7144176165949063
Related functions

dist_pareto_range

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_range(1.0, 3.0);

Output

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

dist_pareto_sample

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Draw a random value (output varies) 
SELECT dist_pareto_sample(1.0, 3.0);
Related functions

dist_pareto_skewness

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_skewness(1.0, 5.0);

Output

dist_pareto_skewness(1.0, 5.0)
4.6475800154489
Related functions

dist_pareto_stddev

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_stddev(1.0, 5.0);

Output

dist_pareto_stddev(1.0, 5.0)
0.3227486121839514
Related functions

dist_pareto_support

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_support(1.0, 3.0);

Output

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

dist_pareto_variance

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

Positional arguments are (scale, shape), both positive and finite. The v1.5 source fix dated October 7, 2026 corrects the older misleading [shape, minimum] parameter labels without changing the runtime order.

1 Corrected v1.5 source (October 7, 2026) 
SELECT dist_pareto_variance(1.0, 5.0);

Output

dist_pareto_variance(1.0, 5.0)
0.10416666666666667
Related functions