Fast arbitrary distribution random sampling (inverse transform sampling)
performance, python, random
Solution
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
Problem
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`?