Generating a triangular distribution in Matlab

问题

I have attempted to generate a triangular probability distribution in Matlab, but was not successful. I used the formula at http://en.wikipedia.org/wiki/Triangular_distribution.

n = 10000000;

a = 0.2;
b = 0.7;
c = 0.5;

u = sqrt(rand(n, 1));

x = zeros(n, 1);
for i = 1:n
    U = u(i);
    if U < (c-a)/(b-a)
        X = a + sqrt(U*(b-a)*(c-a));
    else
        X = b - sqrt((1-U)*(b-a)*(b-c));        
    end
    x(i) = X;
end

hist(x, 100);

The histogram looks like so:

Doesn't look like much of a triangle to me. What's the problem? Am I abusing rand(n)?

回答1:

you can add up two uniform distributions, the distribution graphs convolve, and you get a triangular distribution.

easy-to-understand example: rolling two dice, each action has uniform distribution to result in a number from 1-6, combined action has triangular distribution to result in a number 2-12

edit: minimal working example:

a=randint(10000,1,10);
b=randint(10000,1,10);

c=a+b;

hist(c,max(c)-min(c)+1)

edit2: looked in your script again. It's working but you've made one mistake:

u = sqrt(rand(n, 1));

should be

u = rand(n, 1);

~~edit3: optimized code~~

n = 10000000;

a = 0.2;
b = 0.7;
c = 0.5;

u = rand(n, 1);
x = zeros(n, 1);

idx = find(u < (c-a)/(b-a));
x(idx) = a + sqrt(u(idx)*(b-a)*(c-a));
idx =setdiff(1:n,idx);
x(idx) = b - sqrt((1-u(idx))*(b-a)*(b-c));
hist(x, 100);

回答2:

This example uses the makedist() and pdf() commands.

a = 2; m = 7; b = 10;
N = 50000;                             % Number of samples
pd = makedist('Triangular',a,m,b);     % Create probability distribution object

T = random(pd,N,1);                    % Generate samples from distribution

Triangular Distribution with lowerbound a = 7, mode m = 10, and upperbound b = 10.

% Plot PDF & Compare with Generated Sample
X = (a-2:.1:b+2);

figure, hold on, box on
histogram(T,'Normalization','pdf') % Note normalization-pdf option name-value pair
title([num2str(N) ' Samples'])
plot(X,pdf(pd,X),'r--','LineWidth',1.8)
legend('Empirical Density','Theoretical Density','Location','northwest')

MATLAB introduced makedist() in R2013a. Requires Stats toolbox.

Reference:
Triangular Distribution