python - Fast arbitrary distribution random sampling (inverse transform sampling)

Question

The random module (http://docs.python.org/2/library/random.html) has several fixed functions to randomly sample from. For example random.gauss will sample random point from a normal distribution with a given mean and sigma values.

I'm looking for a way to extract a number N of random samples between a given interval using my own distribution as fast as possible in python. This is what I mean:

def my_dist(x):
    # Some distribution, assume c1,c2,c3 and c4 are known.
    f = c1*exp(-((x-c2)**c3)/c4)
    return f

# Draw N random samples from my distribution between given limits a,b.
N = 1000
N_rand_samples = ran_func_sample(my_dist, a, b, N)

where ran_func_sample is what I'm after and a, b are the limits from which to draw the samples. Is there anything of that sort in python?

Answer 1

You need to use Inverse transform sampling method to get random values distributed according to a law you want. Using this method you can just apply inverted function to random numbers having standard uniform distribution in the interval [0,1].

After you find the inverted function, you get 1000 numbers distributed according to the needed distribution this obvious way:

[inverted_function(random.random()) for x in range(1000)]

More on Inverse Transform Sampling:

• http://en.wikipedia.org/wiki/Inverse_transform_sampling

Also, there is a good question on StackOverflow related to the topic:

• Pythonic way to select list elements with different probability