How do I generate a random number with beta distribution?

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Ana Carolina da Silva Pacheco 2021-4-20

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评论： Ana Carolina da Silva Pacheco 2021-4-21

采纳的回答： Andrew Newell

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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Andrew Newell 2021-4-20

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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 2021-4-20

Because in MATLAB's definition of the beta distribution, the exponents are

and

. So that gives you back

and

.

Ana Carolina da Silva Pacheco 2021-4-21

Got it, thank you, that solved my problem.

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