Convolution and convolution-root properties of long-tailed distributions

Subordination and Superordination Properties for Convolution Operator

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

On Generalized Gamma Convolution Distributions

We present here characterizations of certain families of generalized gamma convolution distributions of L. Bondesson based on a simple relationship between two truncated moments. We also present a list of well-known random variables whose distributions or the distributions of certain functions of them belong to the class of generalized gamma convolutions. Mathematics Subject Classification 2000...

Convolution and Homogeneous Spaces

On Max-sum Equivalence and Convolution Closure of Heavy-tailed Distributions and Their Applications

In this paper, we discuss max-sum equivalence and convolution closure of heavy-tailed distributions. We generalize the well-known max-sum equivalence and convolution closure in the class of regular variation to two larger classes of heavy-tailed distributions. As applications of these results, we study asymptotic behaviour of the tails of compound geometric convolutions, the ruin probability in...

On the Convolution of Gamma Distributions

In this paper, we give a formula for the distribution of the sum of n independent random variables with gamma distributions. A formula for such a sum was provided by Mathai (see [5]) in 1982. But it was complicated. In the paper [1], Jasiulewicz and Kordecki derived a formula for the particular case of independent random variables having Erlang distributions by using Laplace transform. Our meth...