We obtain limit theorems for the row extrema of a triangular array of zero-modified geometric random variables. Some of this is used to obtain limit theorems for the maximum family size within a generation of a simple branching process with varying geometric offspring laws.

Strong convergence, and a weak limit theorem, are obtained for a scheme of 'renormalized' order statistics whose distribution functions are defined by a scheme of functional iteration.

Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n -- [infinity]. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing...

This paper offers a simple proof based on random variable representations for a mixture representation of symmetric Linnik laws previously derived by purely analytic means. The new approach can be set in a much more general context which embraces the symmetric and the positive generalized Linnik...

In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of...

In this paper we discuss the asymptotic behaviour of random contractions X=RS, where R, with distribution function F, is a positive random variable independent of S[set membership, variant](0,1). Random contractions appear naturally in insurance and finance. Our principal contribution is the...