Random Numbers from a Discrete Distribution

Simple algorithm to generate random numbers from a user-defined discrete probability distribution.


Updated 21 Mar 2012

View License

GENDIST - generate random numbers according to a discrete probability distribution
Tristan Ursell, 2011.

T = gendist(P,N,M)
T = gendist(P,N,M,'plot')

The function gendist(P,N,M) takes in a positive vector P whose values form a discrete probability distribution for the indices of P. The function outputs an N x M matrix of integers corresponding to the indices of P chosen at random from the given underlying distribution.

P will be normalized, if it is not normalized already. Both N and M must be greater than or equal to 1. The optional parameter 'plot' creates a plot displaying the input distribution in red and the generated points as a blue histogram.

Conceptual EXAMPLE:

If P = [0.2 0.4 0.4] (note sum(P)=1), then T can only take on values of 1, 2 or 3, corresponding to the possible indices of P. If one calls gendist(P,1,10), then on average the output T should contain two 1's, four 2's and four 3's, in accordance with the values of P, and a possible output might look like:

T = gendist(P,1,10)
T = 2 2 2 3 3 3 1 3 1 3

If, for example, P is a probability distribution for position, with positions X = [5 10 15] (does not have to be linearly spaced), then the set of generated positions is X(T).


P = rand(1,50);
T = gendist(P,100,1000,'plot');


X = -3:0.1:3;
P = 1+sin(X);
T = gendist(P,100,1000,'plot');
Xrand = X(T);

Cite As

Tristan Ursell (2023). Random Numbers from a Discrete Distribution (https://www.mathworks.com/matlabcentral/fileexchange/34101-random-numbers-from-a-discrete-distribution), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2009b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Find more on Creating and Concatenating Matrices in Help Center and MATLAB Answers

Inspired: Random Sample from Discrete PDF

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes

plot fixed

replaced older for loop implementation with histc implementation

minor code reorganization, a little faster, a little cleaner.