beta distribution define !

sample 10000 values from the beta distribution

In each case, count the number of pairs you need to generate until you find 10000 succesful ones.

for alpha = 2 beta = 3 and . Plot the density curve using the plot function and the histogram derived from your samples.

This is the matlab code to find 1 succesful one, but i need to find 10000 and count the pairs needed to get them,

alpha=2; beta=3; a=0; b=1; c=2.5;

X=0; Y=c; % Initial values

while Y > gamma(alpha+beta)/gamma(alpha)/gamma(beta)*X.^(alpha-1).*(1-X).^(beta-1))

U=rand; V=rand; X=a+(b-a)*U; Y=c*V;

end; X

I cant use any other random number generator, the problem is i dont know how to generate 10000 samples with a loop

Answer 1

[Balaji]

Hello Pablo,

I understand that you want to generate 10,000 samples from the beta distribution using the acceptance-rejection method.

You can use a while loop to keep generating pairs until you have enough successful ones. I suggest you to refer to the following code for reference:

alpha = 2; beta = 3; a = 0; b = 1; c = 2.5;
successful_samples = 0;
total_pairs = 0;
samples = zeros(1, 10000);

while successful_samples < 10000
    U = rand;
    V = rand;
    X = a + (b - a) * U;
    Y = c * V;
    
    % Check if the generated point (X, Y) is under the beta PDF curve
    if Y <= (gamma(alpha + beta) / (gamma(alpha) * gamma(beta))) * X^(alpha - 1) * (1 - X)^(beta - 1)
        successful_samples = successful_samples + 1;
        samples(successful_samples) = X;
    end
    
    total_pairs = total_pairs + 1;
end

% Now you have 10,000 samples in 'samples' and the number of pairs generated in 'total_pairs'

% Plot the density curve
x_values = linspace(0, 1, 100);
pdf_values = betapdf(x_values, alpha, beta);
figure;
plot(x_values, pdf_values, 'LineWidth', 2);
hold on;

% Plot the histogram of the samples
histogram(samples, 'Normalization', 'pdf'); 
legend('Beta PDF', 'Histogram of Samples');
title('Density Curve and Histogram of Beta Distributed Samples');
xlabel('Value');
ylabel('Density');

Hope this helps,

Balaji