Is there a method to do arithmetic with SciPy's random variables?

Question

SciPy's stats module have objects of the type "random variable" (they call it rv_frozen). It makes it easy to plot, say, cdf's of random variables of a given distribution. Here's a very simple example:

import scipy.stats as stats
n = stats.norm()
x = linspace(-3, 3)
y = n.cdf(x)
plot(x, y)

I wondered whether there's a way of doing basic arithmetic manipulations on such random variables. The following example is a wishful thinking (it doesn't work).

du_list = [stats.randint(2, 5) for _ in xrange(100)]
du_avg = sum(du_list) / len(du_list)
x = linspace(0, 10)
y = du_avg.cdf(x)
plot(x, y)

This wishful-thinking example should produce the graph of the cumulative distribution function of the random variable which is the average of 100 i.i.d. random variables, each is distributed uniformly on the set {2,3,4}.

Answer 1

I realize this is a bit late, but I figured I'd answer in case anyone else needs this in the future. I needed the same functionality recently and even thought about extending scipy's rv_discrete to implement this, but then I found PaCAL.

PaCAL is a Python software package for doing arithmetic on random variables and it supports quite a few distributions, including continuous distributions. There is even some support for bivariate joint distributions. Available as a package on PyPI. Only for Python 2.x though.

EDIT: The PaCAL repo on Github now supports Python 3.x as well.