MATLAB code to Generate Raleigh Random Variable

[neeraj.patel1]

What is the Matlab code for generating 100,000 Raleigh Random Variable with sigma^2=2 using rand command only. Generate histogram and normalize it by dividing 1,00,000 times the bin width

 

[Pythagorean]

read about these functions:

raylrnd - Rayleigh random generator:
http://www.mathworks.com/help/toolbox/stats/raylrnd.html

hist - for histograms
http://www.mathworks.com/help/techdoc/ref/hist.html

 

[neeraj.patel1]

MATLAB code to find ratio of pair of uniform RV

Homework Statement

Generate 100000 pairs of Uniform RV. Find ratio of each pair of RV.Plot histogram and compare to standard Cauchy density.

Homework Equations

rand()
box muller
cauchy=1/pi*(1+x^2)
hist()

The Attempt at a Solution

use box muller to generate rv

 

[berkeman]

(two similar threads merged)

 

[DeeNos]

The MATLAB code for generating 100,000 Raleigh random variables with sigma^2=2 using the rand command would look something like this:

% Set sigma^2 value
sigma = 2;

% Generate 100,000 random numbers using the rand command
r = sqrt(-2*sigma^2*log(1-rand(1,100000)));

% Plot histogram and normalize it
histogram(r, 'Normalization', 'probability');

% Calculate bin width
bin_width = (max(r)-min(r))/sqrt(length(r));

% Normalize histogram by dividing by 100,000 times the bin width
histogram(r, 'Normalization', 'probability', 'BinWidth', bin_width/100000);

This code first sets the sigma^2 value and then uses the rand command to generate 100,000 random numbers. The Raleigh random variable is calculated using the formula r = sqrt(-2*sigma^2*log(1-rand(1,100000))). Then a histogram is plotted and normalized using the probability option. Finally, the bin width is calculated and the histogram is normalized again by dividing by 100,000 times the bin width to ensure that the histogram is properly normalized. This code can be modified to generate any number of Raleigh random variables with different sigma^2 values.