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...

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 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 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) .

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.

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 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).

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 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).