Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Sorry if it is not an appropriate place for such questions, but anyway can anybody please confirm that the formula for the density function of the four-parameter Beta distribution is correct in Wikipedia. It seems $(c - a)$ is missing in the denominator. Thank you.

Best regards, Ivan

share|cite|improve this question
Such questions are ok; there was a discussion about (more-or-less) similar questions: Questions concerning editing of wikipedia articles. – Martin Sleziak Aug 6 '12 at 16:13
up vote 2 down vote accepted

Yes, the factor is indeed missing.

Let $X$ be standard 2-parameter Beta random variable. The four-parameter one $Y$ is obtained by affine transformation $Y = (c-a) X + a$ for $c>a$. Then $$ f_Y(y) = \frac{1}{c-a} f_X\left(\frac{y-a}{c-a}\right) = \frac{1}{c-a} \left(\frac{y-a}{c-a} \right)^{\alpha-1} \left(\frac{c-y}{c-a} \right)^{\beta-1} \frac{\mathbf{1}(a < y <c)}{B(\alpha,\beta)} = \frac{(y-a)^{\alpha-1} (c-y)^{\beta-1}}{(c-a)^{\alpha+\beta-1}}\frac{\mathbf{1}(a < y <c)}{B(\alpha,\beta)} $$

share|cite|improve this answer
Thanks. If anybody knows how to fix it in Wikipedia, can you please do it? – Ivan Aug 6 '12 at 18:27
@Ivan: Done. It's straightforward to contribute to Wikipedia, by the way; just click on the "edit" link; you can fix things without registering if you want. – joriki Aug 6 '12 at 18:50
@joriki : I was about to say all you need to do is click on "edit" and then edit, but I see you beat me to it. I've actually heard professors say they'd like to change things in Wikipedia articles but they don't know how. – Michael Hardy Aug 6 '12 at 22:18

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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