If X1 and X2 are independent and identically distributed (i. i. d.) with finite variance, then (X1+X2)/[radical sign]2 has the same distribution as X1 if and only if X1 is normal with mean zero (Pólya [9]). The idea of using linear combinations of i. i. d. random variables to characterize the...

Based on inverse Gaussian random variables being transformations of skew-normal random variables, multivariate inverse Gaussian densities are obtained from appropriate multivariate skew-normal distributions. The new skew-normal distributions have some closure properties not satisfied by other...

Two new concepts of order statistics for multivariate samples are introduced. In one of the versions it turns out that not every multivariate order statistic is present in every sample. These order statistics have application in multivariate ranked set sampling and can be used to generate broad...

It is well known that full knowledge of all conditional distributions will typically serve to completely characterize a bivariate distribution. Partial knowledge will often suffice. For example, knowledge of the conditional distribution of X given Y and the conditional mean of Y given X is often...

Distributions with normal conditionals have biquadratic regression functions. Consequently, in contrast to classical bivariate normal distributions, their densities can be multimodal. Criteria for determining the number of modes are discussed and illustrations of representative multimodal...

A goodness of fit test for the Pareto distribution, when the observations are subjected to Type II right censoring is proposed. The test statistic involves transformations of the original data and is based on the nonparametric Nelson-Aalen estimator of the cumulative hazard function. By Monte...