We study d-variate L2-approximation for a weighted unanchored Sobolev space having smoothness m ≥ 1. Folk wisdom would lead us to believe that this problem should become easier as its smoothness increases. This is true if we are only concerned with asymptotic analysis: the nth minimal error is of order n for any δ > 0. However, it is unclear how long we need to wait before this asymptotic behav...

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate generalized exponential-logarithmic, bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as specia...

Abstract: QQ-plots are extremely useful in univariate data analysis. In this article, Koltchinskii (1997) and Chaudhuri’s (1996) definition of multivariate quantile is used to develop analogous plots for bivariate data. Bivariate qq-plots are exhibited for comparing a sample to a given population distribution (the bivariate normal), and for comparing two or more bivariate samples. The plots are...

Motivated by problems of modeling torsional angles in molecules, Singh et al. (2002) proposed a bivariate circular model which is a natural torus analogue of the bivariate normal distribution and a natural extension of the univariate von Mises distribution to the bivariate case. In this paper, we propose a multivariate extension of the bivariate model of Singh et al. The results about condition...

Recently, Sarmanov’s family of bivariate distributions gained interest due to its flexible structure that easily joins given marginals. In this paper, we focus on the parameters estimation for the bivariate Sarmanov distribution with normal-type marginals. The maximum likelihood method is discussed and illustrated on both real and simulated data.