ParetoPickandsDistribution

ParetoPickandsDistribution[μ,σ,ξ]

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

ParetoPickandsDistribution[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:

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Hazard function for the standard ParetoPickands distribution:

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Mean of the ParetoPickands distribution:

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Standard deviation of the ParetoPickands distribution:

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Median of the ParetoPickands distribution:

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Scope  (7)

Applications  (2)

Properties & Relations  (8)

Possible Issues  (1)

Introduced in 2019
(12.0)