Generating Random Numbers from a Generalized Pareto Distribution

Questions
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1

Dear community members,
I’m trying to apply Extreme Value Theory to measure operational risks using Mathematica and I’d like to generate some random numbers following a Generalized Pareto Distribution with 3 parameters: location, scale and shape. I know that Mathematica has 4 different types of Pareto Distribution but as far as I know they are different from the Generalized Pareto one.
Does anybody know how I could do it?
Many thanks in advance,
Ruben

2

You can use a function such as

ranGenPareto = 
  Compile[{{loc, _Real}, {scale, _Real}, {shape, _Real}},
   Module[
    {u},
    u = RandomReal[];
    loc + scale*(u^(-shape) - 1)/shape
    ],
   CompilationTarget -> "C", RuntimeAttributes -> {Listable}
   ];

to generate random numbers from the distribution. The above assumes you have a C compiler on your computer to speed up things.

3

Dear Asim,
thanks a lot for the answer.
Regards,
Ruben

4

CDF[ParetoDistribution[[Sigma], 1/[Xi], [Gamma], [Mu]], x]

gives the CDF as it says under ‘Characterization’ on the Wikipedia page. You can use RandomVariate to create random numbers based on this distribution.