In [16], the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) a...

After having closely re-examined the notion of a Lévy’s stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a stable vector may not only have distinct ...

Generalized exponential distribution has received some attention in the last few years. Recently Kundu and Gupta (2011) and Shoaee and Khorram (2012) introduced an absolute continuous bivariate generalized exponential distribution. In this paper we propose an absolute continuous multivariate generalized exponential distribution. The proposed distribution is very flexible, and the joint probabil...

• The distribution of the variables that originates from monitoring the variance when the mean encountered a sustained shift is considered — specifically for the case when measurements from each sample are independent and identically distributed normal random variables. It is shown that the solution to this problem involves a sequence of dependent random variables that are constructed from inde...

In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regimes models with generalized hyperbolic errors and in the semiparametric switching regimes models of Heckman (1990). Our results for parametric switching regimes models with generalized hyperbolic errors extend some existing results for Ga...