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

[Lionel B]

On Fri, 20 Apr 2007 04:49:50 -0700, Huddwah wrote:

> Hello,
> 
> I would like to create a large random dataset and be able to specify the
> Std Dev., Mean, Kurtosis & Skewness.
> 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.

Note that a normal distribution has zero skew (as does any distribution 
symmetric about its mean) and zero kurtosis[1], so you will have to use a 
different distribution. Perhaps the nearest to a family of distributions 
with parametrisable higher moments might be the "Pearson type IV" 
distribution:

http://en.wikipedia.org/wiki/Pearson_distribution

...but I've absolutely no idea how you'd go about simulating these.

[1] In some definitions of kurtosis a normal distribution has kurtosis 3. 
The 3 is "usually" subtract precisely so that a normal distribution has 
zero kurtosis! This is sometimes known as "excess kurtosis".

[...]

-- 
Lionel B