# How do I generate a random number with beta distribution?

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I have a variable with the PDF:
PDF = C . ((f - LB)/D)^alpha . ((UB - f)/D)^beta
Where:
C = 37337
alpha = 3
beta = 813,21
LB (lower bound) = 60000
UB (upper bound) = 2000000
D = UB - LB = 1940000
How do I generate a random number based on it?
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### Akzeptierte Antwort

Andrew Newell am 20 Apr. 2021
You can use the function betarnd, but you'll need to do some normalizing to get it in the standard form used by MATLAB (see Beta distribution). If you define , then x is in the interval as required, so this should generate a suitable number:
a = alpha+1;
b = beta+1;
r = betarnd(a,b);
your_random_number = r*D+LB;
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Andrew Newell am 20 Apr. 2021
Because in MATLAB's definition of the beta distribution, the exponents are and . So that gives you back and .
Got it, thank you, that solved my problem.

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