Generate Random Number in Range from Single-Tailed Distribution with Python

Question

I want to generate a random float in the range [0, 1) from a one-tailed distribution that looks like this

The above is the chi-squared distribution. I can only find resources on drawing from a uniform distribution in a range, however.

Answer 1

You could use a Beta distribution, e.g.

import numpy as np

np.random.seed(2018)
np.random.beta(2, 5, 10)
#array([ 0.18094173,  0.26192478,  0.14055507,  0.07172968,  0.11830031,
#        0.1027738 ,  0.20499125,  0.23220654,  0.0251325 ,  0.26324832])

Here we draw numbers from a Beta(2, 5) distribution

The Beta distribution is a very versatile and fundamental distribution in statistics; without going into any details, by changing the parameters alpha and beta you can make the distribution left-skewed, right-skewed, uniform, symmetric etc. The distribution is defined on the interval [0, 1] which is consistent with what you're after.

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A more technical comment

While the Kumaraswamy distribution certainly has more benign algebraic properties than the Beta distribution I would argue that the latter is the more fundamental distribution; for example, in Bayesian inference, the Beta distribution often enters as the conjugate prior when dealing with binomial(-like) processes.

Secondly, the mean and variance of the Beta distribution can be expressed quite simply in terms of the parameters alpha, beta; for example, the mean is simply given by alpha / (alpha + beta).

Lastly, from a computational and statistical inference point of view, fitting a Beta distribution to data is usually done in a few lines of code in Python (or R), where most Python libraries like numpy and scipy already include methods to deal with the Beta distribution.