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Random integers with given probabilities ( (v2.0)



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RANDP - pick random values with relative probability

R = RANDP(PROB,..) returns integers in the range from 1 to
NUMEL(PROB) with a relative probability, so that the value X is
present approximately (PROB(X)./sum(PROB)) times in the matrix R.

All values of PROB should be equal to or larger than 0.

RANDP(PROB,N) is an N-by-N matrix, RANDP(PROB,M,N) and
RANDP(PROB,[M,N]) are M-by-N matrices. RANDP(PROB, M1,M2,M3,...) or
RANDP(PROB,[M1,M2,M3,...]) generate random arrays.
RANDP(PROB,SIZE(A)) is the same size as A.

R = randp([1 3 2],1,10000) ;
% return a row vector with 10000 values with about 16650 two's
histc(R,1:3) ./ numel(R)

R = randp([1 1 0 0 1],10,1)
% 10 samples evenly drawn from [1 2 5]

% randomly select 100 elements according to a specific distribution
V = {'Red','Green','Blue'} ;
ind = randp([80 10 10],200,1) ;
R = V(ind) ; % should contain about 160 'Red'


version 2.0, feb 2009

Comments and Ratings (8)

Thanks for this file! Works great!


Martin (view profile)

What an elegant piece of code! Thanks for this.

I've tried this small experiment:

N = 100000; % sample size
w = 1:100; % quite steep distribution
w = w / sum(w); % distribution (pdf)
Y_std = sqrt(w .* (1 - w)); % Standard deviations associated to each probability


Y1 = randp(w, N, 1); % Try Jos function
Y1_w = histc(Y1, [1:100]); % absolute frequencies table
Y1_w = Y1_w / N; % transform into relative frequencies
Y1_w_std = sqrt(Y1_w .* (1 - Y1_w)); % Empirical standard deviations associated to each probability


Y2 = gDiscrPdfRnd(w, N, 1); % Try Gianluca Dorini's function
Y2_w = histc(Y2, [1:100]); % absolute frequencies table
Y2_w = Y2_w / N; % transform into relative frequencies
Y2_w_std = sqrt(Y2_w .* (1 - Y2_w)); % Empirical standard deviations associated to each probability


% Check if empirical standard deviations are coherent with theretical ones
plot(Y_std - Y1_w_std', '.b') % plot empirical differences for Jos function
hold on
plot(Y_std - Y2_w_std', '.r') % plot empirical differences for Gianluca Dorini's function


It looks as though both functions statistically behave very well. They are both excellent functions. Thank you.

Wow, it really is a nice function, very fast and efficient. It is exactly what I was looking for. Thank you.

Carlos Baiz

Works great!

Reza Farrahi Moghaddam

Very useful when dealing with user-defined PDFs.

urs (us) schwarz

nicely coded snippet
two (unimportant) comments:
1) why not put the validity test for P BEFORE the (potentially consuming) generation of all the random numbers...
2) why not add a pointer to RANDSAMPLE for those who own the stats tbx...



implementation of faster algorithm using histc


MATLAB Central test

Slightly modified using hints from <us>

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