A multivariate probability model possessing a dependence structure that is reflected in its variance–covariance structure and gamma distributed univariate margins is introduced and studied. In particular, the higher order moments and cumulants, Chebyshevtype inequalities and multivariate probability density functions are derived. The model suggested herein is believed to be capable of describin...

Given n independent random marked d-vectors Xi with a common density, define the measure νn = ∑ i ξi, where ξi is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near Xi. Technically, this means here that ξi stabilizes with a suitable power-law decay of the tail of the radius of stabilization. For bounded test functions f on Rd, we give a law of l...

We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems.

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...

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

Let X = (Xk)k=0,1,... denote the jump chain of the block counting process of the Λ-coalescent with Λ = β(2 − α, α) being the beta distribution with parameter α ∈ (0, 2). A solution for the hitting probability h(n,m) that the chain X ever visits the state m, conditional that it starts in the state X0 = n, is obtained via an analytic method based on generating functions. For α ∈ (1, 2) the result...