Is there a way to make the Beta distribution have support from 0 to 2, instead of 0 to 1?


1 Answer 1


Sure: define the CDF or PDF in terms of

  • $C'(x,\alpha, \beta) = C(x/2, \alpha, \beta)$
  • $P'(x,\alpha,\beta) = P(x/2,\alpha,\beta)/2$

where $C$ and $P$ are the original Beta CDF and PDF and $C'$ and $P'$ are the new ones (and $\alpha$ and $\beta$ are the two shape parameters).

Wikipedia describes a four-parameter beta distribution which includes both an arbitrary scale parameter (which would be 2 in your case) as well as a shift parameter (which would be 0 for you, since you want the left endpoint of the distribution to stay at zero rather than shifting).

  • $\begingroup$ Hi, and please, how to sample having that new CDF? Is there an inverse Beta equation? $\endgroup$
    – rgap
    Sep 8, 2020 at 5:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.