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