# Four-parameter Beta distribution and Wikipedia

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

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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

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 $$f_Y(y) = \frac{1}{c-a} f_X\left(\frac{y-a}{c-a}\right) = \frac{1}{c-a} \left(\frac{y-a}{c-a} \right)^{\alpha-1} \left(\frac{c-y}{c-a} \right)^{\beta-1} \frac{\mathbf{1}(a < y <c)}{B(\alpha,\beta)} = \frac{(y-a)^{\alpha-1} (c-y)^{\beta-1}}{(c-a)^{\alpha+\beta-1}}\frac{\mathbf{1}(a < y <c)}{B(\alpha,\beta)}$$