Generate synthetic data (or probability distribution object) from user-defined distribution function

John Michell answered . 2025-07-04 08:40:57

% Lomax PDF parameters:
m = 1;
a = 2;
% Draw random samples from uniform distribution in range 0 to 1:
n_samples = 100000;
r = rand(n_samples,1);
% Find the CDF values corresponding to the samples
x = m*((1 - r).^(-1/a)-1);  % Inverse Lomax CDF

% Calculate histogram with bin width 0.1:
binwidth = 0.1;
bins = 0:0.1:5;
N = histcounts(x,bins);  % Number of x values in each bin
f = N/n_samples/binwidth; % Observed frequency per x unit 
bin_centres = (bins(1:end-1)+bins(2:end))/2;''
figure;
bar(bin_centres,f)

% Compare with analytic pdf
x = 0.05:0.1:4.95;
p = a/m*(1+x/m).^-(a+1);   %Lomax PDF
hold on;
h = plot(x,p,'ok');  % Plot the PDF using circles
set(h,'MarkerFaceColor','w')
hold off
str = sprintf('Lomax PDF, m = %3.1f, a = %3.1f',m,a);
title(str)
legend('Sampled','Analytical')

 

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