Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptoticâ€¦ (More)

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 âˆˆ (0, 1). Random contractionsâ€¦ (More)

Let X, Y, B be three independent random variables such that X has the same distribution function as Y B. Assume that B is a beta random variable with positive parameters Î±, Î² and Y has distributionâ€¦ (More)

Let X1, X2, . . . be independent copies of a random variable X whose distribution function is denoted by F. There have been many studies on characterizations of F via linear regression relations ofâ€¦ (More)

A Markov branching process with instantaneous immigration from the zero state can be constructed so as to be honest and have the non-negative integers as state-space, but the construction requiresâ€¦ (More)

A dual Markov branching process (DMBP) is by definition a Siegmundâ€™s predual of some Markov branching process (MBP). Such a process does exist and is uniquely determined by the so-calledâ€¦ (More)

The time to extinction of a subcritical Galton-Watson branching process and the time of last mutation of its infinite-alleles version are maxima of independent random variables having an upper tailâ€¦ (More)

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 aâ€¦ (More)