How do I create a random number generator using congruent method

I want to create a random number generator that uses a congruent method. And I need to create a histogram that should have 0.2 for 1, 0.4 for 2 and 0.4 and 3. When I use rand the histogram works right.

The code I used was this:

prod_total = [];

for j = 1:1000
    x0 = 4;
    m = 5;
    vetor_aleatorio = [ ];
    for k = 1:100
        [u1, x0] = n_aleatorio(x0, k, m);
        vetor_aleatorio(k) = u1;
    end
    
    x = rand;
    
    if (x <= 0.2)
        prod = 1;
    elseif (x > 0.2 &  x <= 0.6)
        prod = 2;
    elseif (x > 0.6 & x <= 1)
        prod = 3;
    end
    prod_total = [prod_total, prod]; 
    
end

histogram(prod_total)

Answer 1

[Jan]

A very cheap linear congruential RNG with parameters suggested by Knuth:

function a = rng_cheap
% On-line Numerical Recipes in C
% http://lib-www.lanl.gov/numerical/bookcpdf.html

% Knuth suggests a = 1664525 as a suitable multiplier for this value of m. H.W. Lewis
% has conducted extensive tests of this value of a with c = 1013904223, which is a prime close
% to m*sqrt(5)/2. The resulting in-line generator (we will call it ranqd1) is simply
%
% unsigned long idum;
% idum = 1664525L*idum + 1013904223L;
%
% This is about as good as any 32-bit linear congruential generator, entirely adequate for many
% uses. And, with only a single multiply and add, it is very fast.
% To check whether your machine has the desired integer properties, see if you can
% generate the following sequence of 32-bit values (given here in hex): 00000000,
% 3C6EF35F, 47502932, D1CCF6E9, AAF95334, 6252E503, 9F2EC686, 57FE6C2D,
% A3D95FA8, 81FDBEE7, 94F0AF1A, CBF633B1.

persistent idum
if isempty(idum)
   idum = 0;
end

idum = rem(1664525 * idum + 1013904223, 4294967296);
a    = idum;  % 32 bit integer 0:2^32-1

% a = idum / 4294967295;  % Double with 32 bit resolution, [0,1]
% a = idum / 4294967296;  % Double with 32 bit resolution, [0,1)

end

[Pedro Almeida]

just a question, this follows a uniform distribution right?

[Jan]

I've included a link as source of this code. You can find the details there. I do not dare to comment comments of Donald E. Knuth.

Answer 2

[Steven Lord]

If this is not for a homework assignment, either use one of the existing random number generators in MATLAB (as listed on this documentation page the 'mcg16807' generator is a multiplicative congruential generator, though it has a very short period) via the rng function or use discretize to convert the uniform numbers from a call to rand into your desired distribution.

weights = [0.2, 0.4, 0.4];
breakpoints = cumsum([0, weights]);
breakpoints(end) = 1;
uniformData = rand(1, 1e6);
discretizedData = discretize(uniformData, breakpoints);
histogram(discretizedData, Normalization="probability");
yline([0.2 0.4], 'r:')

Those look in pretty good agreement with the weights vector.