gives a Pareto–Pickands distribution with location parameter μ, scale parameter σ and shape parameter ξ.
gives the standard Pareto–Pickands distribution with zero location and unit scale parameters.
- 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 value in the generalized Pareto distribution is proportional to for and , and for for and . »
- The survival function for value 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.
Examplesopen allclose all
Basic Examples (4)
Compare data histogram to the population PDF:
Model a tail of a power‐tail distribution, e.g. StudentTDistribution:
Properties & Relations (8)
Pareto–Pickands distribution with is equivalent to a UniformDistribution:
Pareto–Pickands distribution with is equivalent to a shifted ExponentialDistribution:
The Pareto–Pickands distribution family includes ParetoDistribution of types I and II:
Standard Pareto–Pickands distribution with a positive shape parameter ξ is a special case of TsallisQExponentialDistribution:
Wolfram Research (2019), ParetoPickandsDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/ParetoPickandsDistribution.html.
Wolfram Language. 2019. "ParetoPickandsDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ParetoPickandsDistribution.html.
Wolfram Language. (2019). ParetoPickandsDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ParetoPickandsDistribution.html