In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In...

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In...

Motivated by and with the aim of generalizing (Bar-Lev and Enis, 1987), we identify various limit laws of certain centralizing transformations of families of random variables by establishing a nontrivial equivalence with limits of their Laplace–Stieltjes transforms evaluated at transformed values.

Consider the sum Z=∑n=1∞λn(ηn−Eηn), where ηn are independent gamma random variables with shape parameters rn0, and the λn’s are predetermined weights. We study the asymptotic behavior of the tail ∑n=M∞λn(ηn−Eηn), which is asymptotically normal under certain conditions. We...

The equation X1X2W( X1+ X2)with W uniform (0,1) distributed and W,X1 and X2 independent, is generalized in several directions. Most importantly, a generalized multiplication operation is used in which subcritical branching processes, both with discrete and continuous state space, play an...

In this paper it is shown that every nonnegative definite symmetric random matrix with independent diagonal elements and at least one nondegenerate nondiagonal element has a noninfinitely divisible distribution. Using this result it is established that every Wishart distribution Wp(k, [Sigma],...