The applicability or terminating condition for the ordinary case of Zeilberger’s algorithm was recently obtained by Abramov. For the qanalogue, the question of whether a bivariate q-hypergeometric term has a qZ-pair remains open. Le has found a solution to this problem when the given bivariate q-hypergeometric term is a rational function in certain powers of q. We solve the problem for the gene...

We define the product distance matrix of a tree and obtain formulas for its determinant and inverse. The results generalize known formulas for the exponential distance matrix. When we restrict the number of variables to two, we are naturally led to define a bivariate analogue of the laplacian matrix of an arbitrary graph. We also define a bivariate analogue of the Ihara-Selberg zeta function an...

Recently Bassan and Spizzichino (1999) have given some new concepts of multivariate aging for exchangeable random variables, such as a special type of bivariate IFR, by comparing distributions of residual lifetimes of dependent components of different ages. In the same vein, we further study some properties of concepts of IFR in the bivariate case. Then we introduce concepts of bivariate DMRL a...

Battle-Lemari e's wavelet has a nice generalization in the bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the lters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass lter when the degree of the bivariate box spline functions increases to 1. The passing and stopping bands of the ideal lter are dependent ...

Elsewhere, I have promoted the notion of (univariate continuous) “transformation of scale” (ToS) distributions which have densities of the form 2g(W(x)) where g is a symmetric distribution and W is a transformation function with a special property. Here, I develop particular bivariate (readily multivariate) ToS distributions. Univariate ToS distributions have a transformation of random variable...

Lavery splines are examined in the univariate and bivariate cases. In both instances relaxation based algorithms for approximate calculation of Lavery splines are proposed. Following previous work Gilsinn, et al. [7] addressing the bivariate case, a rotationally invariant functional is assumed. The version of bivariate splines proposed in this paper also aims at irregularly spaced data and uses...

Bivariate signals arise in many fields such as oceanography, seismology or radar. A bivariate signal (e.g. the electromagnetic wave field) can be either described by a time-evolving real vector [u(t), v(t)] or equivalently by the complex signal x(t) = u(t)+ iv(t), where u(t), v(t) are its components. In many applications, extracting physically interpretable parameters (e.g. polarization propert...

Bivariate Poisson regression models for ratemaking in car insurance has been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivariate Poisson regression models is used to demonstrate that the overdispersion in the data requires m...

A procedure for estimating a bivariate density based on data that may be censored is described After the data are transformed to the unit square the bivariate density is estimated using linear splines and their tensor products The combined procedure yields an estimate of the bivariate density on the original scale which may provide insight about the dependence structure The procedure can also b...

A class of generalized bivariate Marshall–Olkin distributions, which includes as special cases the Marshall-Olkin bivariate exponential distribution and the Marshall-Olkin type distribution due to Muliere and Scarsini (1987), are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with properties related to evolution of dependence along ti...