Under mild assumptions about the interarrival distribution, we derive a modi ed version of the Birnbaum-Saunders distribution, which we call the tBISA, as an approximation for the true distribution of count data. The free parameters of the tBISA are the rst two moments of the underlying interarrival distribution. We show that the density for the sum of tBISA variables is available in closed for...

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbi...

Lens spaces are a family of manifolds that have been source many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients odd-dimensional spheres by free linear action finite cyclic group, allows deeper analysis their structure. In this paper, we consider the problem moments for distance function between randomly selected pairs points on homogeneous...

We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with respect to the number of ascents and occurrence...

In this paper, we discuss about the bivariate generalized Poisson distribution for the cortisol awakening response and multiple sclerosis in humans. Dysregulation of the hypothalamus-pituitary-adrenal (HPA) axis has been frequently been reported in multiple sclerosis (MS). So far, HPA axis function in MS has predominantly been studied under pharmacological stimulation which is associated with a...

where K is a random variable from 0 to N , and k is a particular value of K. Variance is defined as a measure of statistical dispersion [2], essentially measuring how far out from the mean observed results go. It is given by σ = E[(k − μ)] = E[k]− μ (2) For any known distribution, the generating function is G(s) = E[S ] (3) whereG is the function and s is a variable. Therefore, S {S, S, S, ...,...

For a class of skew-normal matrix distributions, the density function, moment generating function and independent conditions are obtained. The noncentral skew Wishart distribution is defined and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart distributed random matrix are established. A new version of Cochran’s theorem is given. For illustration, ...

Tail asymptotics for the supremum of an independent subadditive process are obtained as a function of the logarithmic moment generating function. We use this analysis to obtain large deviations results for queueing networks in their stationary regime. In the particular case of (max,plus)-linear recursions, the rate of exponential decay of the stationary solution can be explicitly computed.

The class of generating functions for completely monotone sequences (moments of finite positive measures on [0, 1]) has an elegant characterization as the class of Pick functions analytic and positive on (−∞, 1). We establish this and another such characterization and develop a variety of consequences. In particular, we characterize generating functions for moments of convex and concave probabi...