how to calculate the rayleigh distribution in matlab

The Rayleigh probability distribution is a continuous probability distribution used to model random variables that arise in various fields such as physics, engineering, and finance. In Matlab, you can calculate the Rayleigh distribution using the raylpdf and raylcdf functions.

Here's an example code block that shows how to generate and plot the Rayleigh distribution:

main.m
% Generate data for Rayleigh distribution
sigma = 2; % scale parameter
x = 0:0.1:10;
rayleigh_data = raylpdf(x, sigma);

% Plot the Rayleigh distribution
figure;
hold on;
plot(x, rayleigh_data, 'LineWidth', 2);
xlabel('x');
ylabel('f(x)');
title('Rayleigh PDF');

% Calculate and plot the cumulative distribution function
rayleigh_cdf = raylcdf(x, sigma);
figure;
hold on;
plot(x, rayleigh_cdf, 'LineWidth', 2);
xlabel('x');
ylabel('F(x)');
title('Rayleigh CDF');
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In this example, sigma is the scale parameter, and x represents the range of values to evaluate the distribution over. raylpdf calculates the probability density function, while raylcdf calculates the cumulative distribution function. The resulting plot displays the PDF and CDF of the Rayleigh distribution.