S. Satheesh

A Note on Maximum and Minimum Stability of Certain Distributions

In the context of stability of extremes of a random variable (r.v.) X w.r.t a discrete r .v. N, we discuss relations between X and N and extend the notions when X is discrete.

Limit Distributions of Random Sums of Z+-Valued Random Variables

In this article, we formulate a transfer theorem in terms of probability generating functions and discuss two approaches to limit distributions of random sums of Z +-valued random variables. We then develop Z +-valued N-ID and ϕ-ID laws.

On distribution functions with completely monotone derivative

A necessary and sufficient condition for the existence of the mean of distributions with completely monotone derivative is given. Distributions with completely monotone hazard rate are identified. Limit distributions of order statistics in a sample from F(x) which has completely monotone derivative is discussed.

A Note on the Gaps in the Support of Discretely Infinitely Divisible Laws

We discuss the nature of gaps in the support of a discretely infinitely divisible distribution from the angle of compound Poisson laws/processes. The discussion is extended to infinitely divisible distributions on the nonnegative real line.