We consider the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence, we and prove an integral representation of the logarithm of the moment sequence in analogy to the Lévy-Khintchine representation. We use the result to construct product convolution semigroups with moments of all orders and to calculate their Mellin transforms. As an applicatio...

statistical frequency analysis is the most common procedure for the analysis of flood data at a gauged location thatin first step it is needed to select a model to represent the population. among them, the central moment has been themost common and widely used, and with the using of computers, the application of the maximum likelihood hasincreased. this research was carried out in order to reco...

A new family of recursive power-series distributions involving the generalized hypergeometric function is proposed. The probability generating and moment generating functions are given; and extensions of the Poisson, geometric, negative binomial, log-series, and generalized Waring distributions are presented as examples.

A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the condi...

We introduce a new generalized transmuted-Weibull distribution and studied some of the mathematical characterizations distribution. The quantile function, entropy, moment, moment generating order statistics are derived. unknown parameters were estimated through maximum likelihood approach. potential flexibility illustrated by comparing it with other known using real-life data sets. Â

We consider a two-dimensional semimartingale reflecting Brownian motion (SRBM) in the nonnegative quadrant. The data of the SRBM consists of a two-dimensional drift vector, a 2 × 2 positive definite covariance matrix, and a 2 × 2 reflection matrix. Assuming the SRBM is positive recurrent, we are interested in tail asymptotic of its marginal stationary distribution along each direction in the qu...

The cumulant generating function of a cost function is the logarithm of the moment generating function of the cost function. The Taylor coefficients of the cumulant generating function are called the cumulants of the cost function. This project is concerned with the optimization of a linear combination of the cumulants of a cost function. The problem is quite general since the coefficients of t...