draw random number following a custom distribution

Question

I need to draw random numbers following a distribution I chose.

Example: draw 7 numbers from 1 to 7 with those probabilities:

1: 0.3
2: 0.2
3: 0.15
4: 0.15
5: 0.1
6: 0.05
7: 0.05

Since in my actual application I need to draw potentially 1000 numbers I need this to be as much efficient as possible (ideally linear). I know there is a function in MATLAB that draws random numbers from a normal distribution; is there any way to adapt it?

See also [Weighted random numbers in MATLAB](http://stackoverflow.com/questions/2977497/weighted-random-numbers-in-matlab). — chappjc, Mar 14 '14 at 19:28

score 8 · Accepted Answer · edited May 23 '17 at 12:21

8

Think you can use randsample too from Statistics Toolbox as referenced here.

%%// Replace 7 with 1000 for original problem
OUT = randsample([1:7], 7, true, [0.3 0.2 0.15 0.15 0.1 0.05 0.05])

edited May 23 '17 at 12:21

Community

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answered Mar 14 '14 at 19:03

Divakar

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I was just answering with this. +1 – chappjc Mar 14 '14 at 19:03
If you check the the distribution, it won't be the requested one. – Robert Seifert Mar 14 '14 at 19:19
3

@thewaywewalk The idea is to draw numbers with a certain probability from a custom distribution, not generate samples that have a specific distribution. Note the OP's comments about the existing function to draw from a normal distribution. – chappjc Mar 14 '14 at 19:22
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+1 I keep forgetting about `randsample` – Luis Mendo Mar 14 '14 at 19:25

score 1 · Answer 2 · answered Mar 14 '14 at 18:57

numbers = 1:7;
probs = [.3 .2 .15 .15 .1 .05 .05];
N = 1000; %// how many random numbers you want

cumProbs = cumsum(probs(:)); %// will be used as thresholds
r = rand(1,N); %// random numbers between 0 and 1
output = sum(bsxfun(@ge, r, cumProbs))+1; %// how many thresholds are exceeded

score 1 · Answer 3 · answered Mar 14 '14 at 18:59

1

You can use gendist from matlab file exchange: http://www.mathworks.com/matlabcentral/fileexchange/34101-random-numbers-from-a-discrete-distribution/content/gendist.m

This generates 1000 random numbers: gendist([.3,.2,.15,.15,.1,.05,.05],1000,1)

answered Mar 14 '14 at 18:59

Daniel

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chappjc · Answer 4 · 2014-03-14T19:49:50.857

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If you do not have randsample, you can use histc like it does internally, just without all the fluff:

N = 100;
nums = 1:7;
p = [.3 .2 .15 .15 .1 .05 .05];

cdf = [0 cumsum(p(:).'/sum(p))]; cdf(end)=1; %' p is pdf
[~, isamps] = histc(rand(N,1),cdf);
out = nums(isamps);

edited Mar 14 '14 at 19:49

answered Mar 14 '14 at 19:09

chappjc

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draw random number following a custom distribution

4 Answers4