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.

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.

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...

We obtain a characterization result for the bivariate negative binomial distribution by using arguments based on bivariate power series families of distributions for α-monotone random variables. This is an extension of a result due to Sapatinas (1999).

We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form where {Wnj, 1[less-than-or-equals, slant]j[less-than-or-equals, slant]n, n[less-than-or-equals, slant]1} and {Xnj, 1[less-than-or-equals, slant]j[less-than-or-equals, slant]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).

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.