# ParetoPickandsDistribution

ParetoPickandsDistribution[μ,σ,ξ]

gives a ParetoPickands distribution with location parameter μ, scale parameter σ and shape parameter ξ.

gives the standard ParetoPickands distribution with zero location and unit scale parameters.

# Details • The ParetoPickandsDistribution is also known as generalized Pareto distribution or GPD.
• ParetoPickandsDistribution allows σ to be any positive real number and μ and ξ to be any real numbers.
• The probability density function for values in the generalized Pareto distribution is proportional to for and , and for for and .  »
• The survival function for values in the generalized Pareto distribution equals for and , and for for and .
• The hazard function for value in the generalized Pareto distribution equals for and , and zero otherwise.  »
• ParetoPickandsDistribution can be used with such functions as Mean, CDF and RandomVariate.

# Examples

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## Basic Examples(4)

Probability density function for the standard ParetoPickands distribution:

 In:= Out= In:= Out= Hazard function for the standard ParetoPickands distribution:

 In:= Out= In:= Out= Mean of the ParetoPickands distribution:

 In:= Out= Standard deviation of the ParetoPickands distribution:

 In:= Out= Median of the ParetoPickands distribution:

 In:= Out= ## Possible Issues(1)

Introduced in 2019
(12.0)