Random Variates when the cumulative distribution is known.

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[Stephen23]

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[Stephen23]

Random Variates when the cumulative distribution is known.

Vinay Ahir on 1st of October 2020 at 14:00:

For a simulation, I need to generate random variate numbers (RVN).

The cumulative distribution F is known and is according the following code:

x=0:(pi/100):pi/2;

F=sin(x); % an always growing curve

I need to generate 2000 random variate number and show the histogram of the numbers.

Answer 1

[Ameer Hamza]

If you have statictics and machine learning toolbox, the try piecewise linear distributon

x=0:(pi/100):pi/2;
PDF = sin(x);
CDF = cumtrapz(x, PDF);
CDF(end) = 1; % requirement of PiecewiseLinear, last element must be exactly 1.

p = makedist('PiecewiseLinear', 'x', x, 'Fx', CDF);
x = random(p, 100000, 1); % generate 100000 samples
histogram(x)

If you don't have toolbox, then use this FEX package: https://www.mathworks.com/matlabcentral/fileexchange/26003-random-numbers-from-a-user-defined-distribution

Also, look at this method: https://en.wikipedia.org/wiki/Inverse_transform_sampling. CDF is easily invertible in this interval, so you can code your own method from scratch too.

[Vinay Ahir]

Thank you so much. Works flawlessly.

[Ameer Hamza]

I am glad to be of help!