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...

Methods to construct max-semi-selfdecompsable laws and their implications in compound extremal processes are discussed. Max-autoregressive model is introduced and characterized using max-semi-selfdecompsable laws. Max-semi-selfdecomposability of max-semi-stable laws is proved.

Generalizations and extensions of a first order autoregressive model of Lawrance and Lewis [Lawrance, A.J., Lewis, P.A.W., 1981. A new autoregressive time series modeling in exponential variables (NEAR(1)). Adv. Appl. Probab. 13, 826-845] are considered and characterized here.

We establish a characterization of the multivariate normal based on a maximal property relating Var[g([zeta])] and the gradient of g(·).

A characterization theorem is proved for a family of non-negative integer valued random variables. The result is based on an inequality of the type proved by Chernoff (1981). Applications of the result for various standard distributions are also discussed.

Stability of the maximum of a random number N of independent identically distributed r.v.'s Xn was discussed by Voorn (1987). We consider a generalized version of this problem and study the connection between the distributions of X1 and N.

We prove the equivalence of the limit distributions of an appropriately centered and normalized sum and the maximum sum of independent random variables which have finite expectations. The result is an extension of a result of Kruglov (1999).