Random Numbers from a Discrete Distribution

Simple algorithm to generate random numbers from a user-defined discrete probability distribution.
Updated 21 Mar 2012

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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 (2024). 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
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Version Published Release Notes

plot fixed

replaced older for loop implementation with histc implementation

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