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

From: Martin Jansche
Subject: Re: [Help-gsl] Random Number Algorithm with specific stats
Date: Thu, 10 May 2007 15:35:58 -0400

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

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