Closeness of Grassia's Transformed Gammas and the Beta Distribution

Summary The flexibility and applicability of the Beta distribution are well known. In this note a comparison is made between the Beta and two other distributions on (0,1) which have been proposed by Grassia (1977) and which are derived through transformation of the Gamma distribution. The extreme closeness of the distributions is demonstrated graphically and explored more formally through a measure of closeness (Kolmogorov‐Smirnov distance). Alternative measures of closeness are also briefly discussed. It is concluded that for many applications the distributions are sufficiently similar (that is, virtually identical) for a choice among them to rest solely on mathematical convenience.