How to pick a value according to its probability

Hi,

Let's say

P = [0.1 0.3 0.4 0.2]
X = [1 2 5 9]

where P(n) is the probability to select the X(n) element. I wish to make a function that select a "random" element of X according to its probability, like

f = myfun(P,X)
>> f = 2  (occurs around 30%)

thx a lot

[Oleg Komarov]

This is a double post. See my comment on Andrei's answer: http://www.mathworks.com/matlabcentral/answers/23319-easy-question-with-probability

[Nikolas Spiliopoulos]

what if we have two numbers? Lets say 50% probability to get a=0.05 and b= -0.05

Sorry I am a very beginner in MATLAB

thanks in advance

Nikolas

[Walter Roberson]

AB = [a,b];
AB( randi([1 2]) )

[PANTHAGADA ANIL KUMAR]

how to select an element with least probablility

Answer 1

[Sean de Wolski]

f = X(find(rand<cumsum(P),1,'first'))

[Walter Roberson]

The answers in the other thread took care in case cumsum(P) < 1 as can happen due to round-off error.

Answer 2

[Jonathan]

The accepted answer is not doing any sanity check, and is sensitive to rounding errors. You should use randsample instead.

To sample n points from X, with replacement, and probabilities P:

randsample( X, n, true, P )

This can also be used with a custom RandStream (see documentation). Be aware that this function does NOT check for negative values in P; check manually if needed.

[Sepehr Saadatmand]

That was what I was looking for. Thank you !

[PANTHAGADA ANIL KUMAR]

how to select an element with least probablility

[krishna teja]

searched a lot for this kind of function

[Real User]

randsample() seems to require Statistics and Machine Learning Toolbox

Answer 3

[Steven Lord]

You can use discretize (which didn't exist when this question was asked originally) to do this. Generate uniform random numbers, bin them using bins whose widths are given by P, and for each bin return the corresponding element of X.

P = [0.1 0.3 0.4 0.2];
X = [1 2 5 9];
values = discretize(rand(1, 1e4), cumsum([0 P]), X);
histogram(values, 'Normalization', 'probability')

The probabilities shown in the histogram should agree pretty closely with the values in P.

Answer 4

[Mendi]

The fastest one (100ns-200ns):

function [idx] = get_random_choice(p)
	% Random choice with probability
	% Example: get_random_choice([0.2,0.7,0.1])
	N=length(p); idx=1; cump=0; 
	r=rand;
	while(idx<N)
		cump=cump+p(idx);
		if(cump>r),break,else,idx=idx+1;end
	end
end