python: random sampling from self-defined probability function [duplicate]

Answer 1

As your function is bounded both in x and p(x), I recommend that you use Monte Carlo rejection sampling. The basic principle is that you draw two uniform random numbers, one representing a candidate x in the x space bounds [0,b] and another representing y. If y is lower or equal to the normalized p(x), then the sampled x is returned, if not it continues to the next iteration

import numpy as np
def rejection_sampler(p,xbounds,pmax):
    while True:
        x = np.random.rand(1)*(xbounds[1]-xbounds[0])+xbounds[0]
        y = np.random.rand(1)*pmax
        if y<=p(x):
            return x

Here, p should be a callable to your normalized piecewise probability density, xbounds can be a list or tuple containing the lower and upper bounds, and pmax the maximum of the probability density in the x interval.