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

[Ralph Silva]

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
> 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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