How to generate a distribution with a given mean, variance, skew and kurtosis in Python?

How about using scipy? You can pick the distribution you want from continuous distributions in the scipy.stats library.

The generalized gamma function has non-zero skew and kurtosis, but you'll have a little work to do to figure out what parameters to use to specify the distribution to get a particular mean, variance, skew and kurtosis. Here's some code to get you started.

import scipy.statsimport matplotlib.pyplot as pltdistribution = scipy.stats.norm(loc=100,scale=5)sample = distribution.rvs(size=10000)plt.hist(sample)plt.show()print distribution.stats('mvsk')

This displays a histogram of a 10,000 element sample from a normal distribution with mean 100 and variance 25, and prints the distribution's statistics:

(array(100.0), array(25.0), array(0.0), array(0.0))

Replacing the normal distribution with the generalized gamma distribution,

distribution = scipy.stats.gengamma(100, 70, loc=50, scale=10)

you get the statistics [mean, variance, skew, kurtosis](array(60.67925117494595), array(0.00023388203873597746), array(-0.09588807605341435), array(-0.028177799805207737)).

Try to use this:

http://statsmodels.sourceforge.net/devel/generated/statsmodels.sandbox.distributions.extras.pdf_mvsk.html#statsmodels.sandbox.distributions.extras.pdf_mvsk

Return the Gaussian expanded pdf function given the list of 1st, 2nd moment and skew and Fisher (excess) kurtosis.

Parameters : mvsk : list of mu, mc2, skew, kurt

Looks good to me. There's a link to the source on that page.

Oh, and here's the other StackOverflow question that pointed me there:Apply kurtosis to a distribution in python