How do I generate a random number with beta distribution?

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?

Answer 1

[Andrew Newell]

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;

[Ana Carolina da Silva Pacheco]

Thank you so much! But why did you add 1 in alpha and beta?

[Andrew Newell]

Because in MATLAB's definition of the beta distribution, the exponents are and . So that gives you back and .

[Ana Carolina da Silva Pacheco]

Got it, thank you, that solved my problem.