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Sampling from a discrete distribution

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Sampling from a discrete distribution

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27 Oct 2008 (Updated )

The function is to draw samples from an arbitrary discrete distribution.

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Description

There are a lot of cases that you might need to sample from a discrete distribution in Monte Carlo simulations. Here are some typical examples that this function may help

(1) you want to sample from a discrete distribution over finitely many categories(labels). However, the pmf is not easy to directly sample from. Then you can just compute p(k) for each category, and then use this function to do the sampling.

(2) For a general (possibly non-parametric) continuous distribution defined in a 1D/2D space, you may discretized the sample space into small regions, and compute the probability mass for these regions, and then use this function to do the sampling.

(3) In many models, the probability distribution is expressed as a weighted sum of several "modes". To sample from this kind of distributions, you may need to first choose which mode to generate the sample according to their weights, then this function may fit in.

In sum, this function can be used directly in simple sampling, and may also be used as a building block of complicated simulation procedure.

The use of this function is easy:

x = discretesample(p, n).

You just input the probability mass, and tell the function how many sample you want to sample, then it returns the samples in form of a 1 x n vector.

Acknowledgements

This file inspired Lynx Matlab Toolbox.

MATLAB release MATLAB 7.6 (R2008a)
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Comments and Ratings (10)
08 Nov 2013 Justin

Very helpful! Thx!

10 Jul 2013 Christos

Very useful, saves a lot of time when it comes in large scale simulation problems.

21 Jun 2012 Woojae Kim

Mo Chen, that is brilliant! That should be the fastest way to get the job done in MATLAB. Thanks!

13 Jan 2012 Thomas Clark

Very useful, a good utility function which saves some though when implementing MC models.

22 Feb 2011 Reza Fathzadeh  
05 Nov 2009 Mo Chen

your function seems to complicate the problem a little bit.
The following line is enough to do the jod
[~,x] = histc(rand(1,n),[0;cumsum(p(:))/sum(p)]);

21 Jun 2009 Carlos Baiz  
29 Oct 2008 Dahua Lin

Jos,

I have checked with randp. Though they seem offering similar functionalities, however, the efficiency is drastically different, especially in very large scale monte carlo simulation, say you need to draw thousands or millions of samples from a distribution over thousands or even millions of states, which is not unusual in real engineering applications.

With randp, it would be incur obvious latency when you want to draw thousands of samples from thousands of states, or even run out of memory (thus resulting an empty matrix), as the algorithm implemented by randp is of complexity O(k n), where k is the number of states in the sample space. However, even million-state-level sampling can be accomplished by this function within milliseconds, as its complexity is only O(n logk).

Hope my explanation can clarify the differences between these two files.

28 Oct 2008 Jos (10584)

if you'd searched before submitting you would have found RANDP on the FEX. What does this function add?

28 Oct 2008 Dahua Lin

There's a bug in the initial submission, which has been fixed, and the new version has been uploaded, which may come out in a day.

Updates
28 Oct 2008

Fixing a bug that may lead to incorrect sampling.

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