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Re: [Help-gsl] Random Number Algorithm with specific stats

From: Ralph Silva
Subject: Re: [Help-gsl] Random Number Algorithm with specific stats
Date: Mon, 14 May 2007 15:02:46 -0300

You can look for the generalized hyperbolic distribution (GHP)
(Barndorff-Nielsen, 1977). It has five parameters. It is quite easy to
sample from it. First from the generalized inverse Gaussian  then from GHD
using normal mean-variance mixture. It has many particular cases including
Student-t, normal and other distributions mentioned in this list.

On 5/10/07, Martin Jansche <address@hidden> wrote:

On 4/20/07, Huddwah <address@hidden> wrote:

> I have coded up a few different random number generators from scratch
> create gaussian/normal distributions. I can get as far as specifying the
> mean and standard deviation but have no idea how to incorporate
> values for Kurtosis and Skewness.

You need a larger family of distributions with at leat four parameters
that will allow you to adjust the first four moments/cumulants
independently of each other.  The Pearson family is such a system:
your position in skewness/kurtosis space determines the exact type of
the Pearson distribution, and for many types (Beta, Gamma, inverse
Gamma) simulation is straightforward using GSL.  Alternatively you
could look into the Johnson family of distributions: since it is based
on transformations of random variables, random number generation is
very easy to do.

-- mj

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