Abstract The reliability properties of beta-transformed random variables are discussed. A necessary and sufficient condition for a beta-transformed geometric random variable to follow a power series distribution is derived. It is shown that a beta-transformed member of the Katz family does not...

We establish a characterization of the multivariate normal based on a maximal property relating Var[g([zeta])] and the gradient of g(·).

Stability of the maximum of a random number N of independent identically distributed r.v.'s Xn was discussed by Voorn (1987). We consider a generalized version of this problem and study the connection between the distributions of X1 and N.

We prove the equivalence of the limit distributions of an appropriately centered and normalized sum and the maximum sum of independent random variables which have finite expectations. The result is an extension of a result of Kruglov (1999).

We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form where {Wnj, 1[less-than-or-equals, slant]j[less-than-or-equals, slant]n, n[less-than-or-equals, slant]1} and {Xnj, 1[less-than-or-equals, slant]j[less-than-or-equals, slant]n,...

We obtain a characterization result for the bivariate negative binomial distribution by using arguments based on bivariate power series families of distributions for α-monotone random variables. This is an extension of a result due to Sapatinas (1999).