random.gauss(mu, sigma)
Above is a function allowing to randomly draw a number from a normal distribution with a given mean and variance. But how can we draw values from a normal distribution defined by more than only the two first moments?
something like:
random.gauss(mu, sigma, skew, kurtosis)
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.stats
import matplotlib.pyplot as plt
distribution = 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))
.