We show that randomly stopped partial sums of nonnegative i.i.d. sequences with a geometric stopping variable, inherit some nonparametric class properties defined via the Laplace ordering and that the corresponding converses also hold. Our findings extend earlier results in this direction...

Let (Xn, n [greater-or-equal, slanted] 1) be a sequence of i.i.d. positive valued random variables with a common distribution function F and let Sn = [Sigma]nj=1 Xj, n [greater-or-equal, slanted] 1. When F belongs to the domain of partial attraction of a positive semi-stable law, Chover's form...

We obtain here the large deviation results for trimmed sums ((r)Sn) of i.i.d. random variables (Xn), with the distribution function belonging to the domain of attraction of a positive stable law. As an application, we establish a law of the iterated logarithm.

Let W(t) be a standard Wiener process and let where at is a nondecreasing function of t with 0 < at [less-than-or-equals, slant] t and t-1at nonincreasing. Let (tk) be some increasing sequence diverging to [infinity]. In this paper we study the almost sure behaviour of lim supk-->[infinity][beta]tk sup0[less-than-or-equals, slant]s[less-than-or-equals, slant]atk W(tk+s) - W(tk) .

Let X(t), t[epsilon][0,[infinity]) be a stable subordinator defined on a probability space ([omega], H, P) and let ar,t0, be a non-negative valued function. Under certain conditions on at, it is shown that there exists a function [beta](t) such that Also, iterated logarithm results for...

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(·).

A characterization theorem is proved for a family of non-negative integer valued random variables. The result is based on an inequality of the type proved by Chernoff (1981). Applications of the result for various standard distributions are also discussed.

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.