Generate Random Numbers

Methods for generating random numbers from a distribution based on random draws from a uniform distribution.

These were developed to debug a python script ported from MATLAB in which many random numbers were generated. Given the same random seed, one can draw the same uniform random numbers in MATLAB and python (using numpy). Unfortunately that doesn’t work for other distribution due to differences in implementation.

Functions

Generate random variates of various distributions based on draws from a uniform distribution See: https://www.cse.wustl.edu/~jain/books/ftp/ch5f_slides.pdf

Given the same random seed, MATLAB and numpy will generate the same draws from a uniform distribution. This isn’t the case for other distributions. Instead, it’s possible to generate other distributions based on U(0, 1) draws. In turn, one can generate the same pseudorandom numbers in MATLAB and numpy using these functions and MATLAB equivalent functions

rand.randombeta(a, b, size=1)

Generate random variates from beta distribution given shape parameters a, b

rand.randombetavariate(a, b)

Generate single random variate from beta distribution given shape parameters a, b

NOTE: only implemented for a < 0 and b < 0

rand.randomexponential(a, size=1)

Generate random variate from exponential distribution. Uses inverse CDF method

pdf: f(x) = (1/a)e^(-x/a)

Parameters:a – scale paramter (a > 0)

rand.randomgammaint(shape, scale=1.0, size=1)

draw from random gamma distribution with integer shape parameter

rand.randomgamma(shape, scale=1.0, size=1, tol=1e-05)

Generate random variates from a gamma distribution

Parameters:

• shape (float or array_like of floats) – Shape of gamma distribution (should be > 0)
• scale (float or array_like of floats) – Scale of the gamma distribution (should be > 0)
• size (int) – number of variates to return

rand.randomnormal(mu, sigma, size=1)

Generate random variate from the normal distribution using the Box Muller technique

Returns:

rand.randombinomial(n, p)

Generate random variates form a binomial(n, p) distribution

Parameters:

• n – number of trials
• p – probability of success

rand.randomdirichlet(a)

Python implementation of randdirichlet.m using randomgamma fucnction

Parameters:a – vector of weights (shape parameters to the gamma distribution)