We introduce a new generalized family of nonnegative continuous distributions by addingtwo extra parameters to a lifetime distribution, called the baseline distribution, by twice com-pounding a power series distribution. The new family, called the lifetime power series-powerseries family, has a...

In this paper, we discuss a generalization of the collective risk model and of Panjer's recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim...

Teicher [1955] proved that the probability a Poisson distribution with mean k takes on a value of k or less is monotonically decreasing in k. I extend this inequality by proving that the probability a Poisson distribution with mean zk takes on a value of k or less is monotonically decreasing for...

The paper focuses on type II Topp-Leone Frechet distribution. Its properties including hazard rate function, reverse hazard rate function, Mills ratio, quantile function and order statistics have been studied. The maximum likelihood estimation used for estimating the parameters of the proposed...

For evaluating the probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based...