A Generalized Dirichlet Distribution in Bayesian Life Testing

Let F(x) be the c.d.f. for some population of life times. For real numbers tl O and F(tk))<1, let Pi = F(tl) and pi = F(ti) F(ti-1) for i = 2, 3, ..., k. A generalized Dirichlet prior distribution for p = (Pl, ...,Pk) having density function f(p) oc Hk 1p'-1 (1 -pl ... p) is considered. An intuitive justification for using this density is given and its properties are studied. Comparisons are made between this distribution and the Dirichlet distribution. The posterior distribution of F(ti) is also considered.