Hi everybody, i wonder if beta distribution is infinitely divisible? Any references on the subject?Thanks.

You can try to check if it's charactristic function has a Levy-Khintchine decomposition. If yes, then it is infinitely divisible.

The Beta-distribution lives on the interval [0,1] so it is impossible to be infinitely divisible. Any distribution on a bounded interval can not be infinitely divisible, other examples are the uniform and the Binomial one. So sorry, no Beta-Levy process exists.

A Beta Distribution is a family of distributions which are non-zero only over a finite interval 0 < X < 1: f(X) = kX^vn-1 (1-X) ^n-1 where k = T (n+m)/T (n) T(m)n and m are positive integers, and is Euler's gamma function. be infinitely decomposable, leading to the concept of a triangular array, defining infinite divisibility: A random variable X is said to be infinitely divisible if there exists a triangular array X11 ; X21 , X22; X31, X32, X33; . . . ; ; Xn1 , Xn2, . . . , Xnn; . . . ,such that X11X21 + X22X21 + X22 + X23 . . .Xn1 + Xn2 + . . . + Xnn. . .are all distributed as X. the infinitely divisible category includes many families of distributions, such as the Normal, Cauchy, and Gamma. It’s essential that infinitely divisible do not seem possible for distributions with limited domain [0,1], rgds.