In this paper we consider compound distributions where the counting distribution is a bivariate distribution with the probability function (Pn,,,2)n,,n2_>0 that satisfies a recursion in the form P""n2 = a°+al +a~2 +n~2/P'"-t'n2-' n2 P,1-1.,,2 qCOW Phi,n2-1, h i , n2 = 1, 2, ... We present an algorithm for recursive evaluation of the corresponding compound distributions and some examples of dist...

On Some Properties of Bivariate Exponential Distributions Qi-Ming He a , Hanqin Zhang b c & Juan C. Vera d a Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada b Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China c NUS Business School, Singapore d Department of Econometrics and Operatio...

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y). The algebraic form for R = Pr(X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X ,Y) follows a bivaria...

The Fisher information matrices for four bivariate Pareto distributions are derived.

The authors examine the asymptotic behaviour of conditional threshold exceedance probabilities for an elliptically distributed pair (X,Y ) of random variables. More precisely, they investigate the limiting behaviour of the conditional distribution of Y given that X becomes extreme. They show that this behaviour differs between regularly and rapidly varying tails. Le comportement extrême des loi...

Expanding upon work by Diessel & Tomasello (2005, hereafter D&T) and Gries (to appear), 1 this study explores particle positioning in child language as a gradual cognitive-pragmatic development based on statistical distribution of input. The phenomenon of particle position alternation is peculiar insofar as it defines a category of combinations which show syntactic variation without concomitant...

In this paper we discuss various definitions of bivariate reversed hazard rate and their properties. An exponential representation of bivariate distribution using reversed hazard rates is given and we also develop a new family of bivariate distributions using bivariate reversed hazard rate. Finally we give a local dependence measure using bivariate reversed hazard rates and study its properties...

Let (RU1, RU2) be a given bivariate scale mixture random vector, with R > 0 being independent of the bivariate random vector (U1, U2). In this paper we derive exact asymptotic expansions of the tail probability P{RU1 > x, RU2 > ax}, a ∈ (0, 1] as x → ∞ assuming that R has distribution function in the Gumbel max-domain of attraction and (U1, U2) has a specific tail behaviour around some absorbin...

We derive bivariate exponential distributions using independent auxiliary random variables. We develop separate models for positive and negative correlations between the exponentially distributed variates. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y = aX +Z where a is a positive constant and Z is independent of X. To obtain exponentia...

In this paper, we descibe the general construction of multivariate phase-type distributions of discret or continuous type and study their commun distributions and densities on lower dimensional subspaces. Finally, we adopt the known EM algorithm for approximating bivariate phase distributions to a set of two-dimensional observations.