I want to generate data in Python that behaves like real stock market data, which means I need to be able to specify and play around with all of the first four moments. Only being able to control skewness or only kurtosis is unfortunately not enough.
I found some answers here: How to generate a distribution with a given mean, variance, skew and kurtosis in Python?, however I seem unable to gain control of the properties with the gengamma distribution.
I know there are tons of distributions here: https://docs.scipy.org/doc/scipy/reference/stats.html#continuous-distributions, maybe I can use one of them in some clever way? Or is there another way?