How to generate random numbers for Beta distribution in a range?

Question

In Excel I can just write:

BETA.INV(RAND(),alpha,beta,lowerbound,upperbound)

To generate a beta distributed random between lower bound and upper bound

How can I do the same in Mathematica?

In other words hat is the right way to scale the output of:

RandomVariate[BetaDistribution[3,3]]

So that instead of generating a number between 0 and 1 it gives me a number between 25 and 73?

In Excel I would just write:

BETA.INV(RAND(),3,3,25,73)

But I don't know what to do in Mathematica

Answer 1

You can just rescale it

RandomVariate[BetaDistribution[3,3]] * (max - min) + min
RandomVariate[BetaDistribution[3,3]] * 48 + 25

A plot:

Show[
 Histogram[Array[RandomVariate[BetaDistribution[3, 3]]*48 + 25 &, 100000], 48,"PDF"],
 Plot[{((1-((x-25)/48))^(-1+3)((x-25)/48)^(-1+3))/(48 Beta[3,3])}, {x, 25,73}]]

Answer 2

Just to illustrate:

• TransformedDistribution

• Rescale

  td[a_, b_, min_, max_, n_] :=
  RandomVariate[
  TransformedDistribution[(max -min) x + min,
  x \[Distributed] BetaDistribution[a, b]], n]
  
  
  rs[a_, b_, min_, max_, n_] := 
  Rescale[RandomVariate[BetaDistribution[a, b], n], {0, 1}, {min, max}]