The joint distribution of order statistics is characterized without reference to a parent distribution. To this end, the possible univariate margins of such a distribution are first determined. The class of possible copulas K is then characterized under the assumption of continuous margins...

A test to assess if a sample comes from a multivariate skew-normal distribution is proposed. The test statistic is obtained from the canonical form of the multivariate skew-normal distribution and its null distribution is derived. The power of the proposed test is evaluated through Monte Carlo...

When an n×1 random vector X=(X1,…,Xn)T has a sign-invariant distribution, Strait (1974) proved that the expectations of max(0,X1,X1+X2,…,X1+Xn) and max(0,X1,…,Xn) are equal. In this note we assume a weaker condition that (X1,X2,…,Xn) and (−X1,X2,…,Xn) are equal in distribution and...

In this work, we introduce the s,k-extremal coefficients for studying the tail dependence between the s-th lower and k-th upper order statistics of a normalized random vector. If its margins have tail dependence then so do their order statistics, with the strength of bivariate tail dependence...

In this paper, we compare the largest order statistics arising from independent heterogeneous gamma random variables based on the likelihood ratio order. Let X1,…,Xn be independent gamma random variables with Xi having shape parameter r∈(0,1] and scale parameter λi, i=1,…,n, and let Xn:n...

We present a method for the obtention of the maximal correlation coefficient that extends the simple method given by Papadatos and Xifara (2013). We illustrate our method with the calculation of the maximal correlation between the kth largest order statistics of overlapping samples.

Huang and Kotz (1999) [17] considered a modification of the Farlie–Gumbel–Morgenstern (FGM) distribution, introducing additional parameters, and paved the way for many research papers on modifications of FGM distributions allowing high correlation. The first part of the present paper is a...

We compare the hazard rate functions of the largest order statistic arising from independent heterogeneous gamma random variables and that arising from i.i.d. gamma random variables. Specifically, let X1,…,Xn be independent gamma random variables with Xi having shape parameter 0r≤1 and scale...

In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this result, some equivalent characterizations of stochastic comparisons of sample ranges with respect...

In this article we obtain the characteristic functions (c.f.'s) for 1-spherical distributions and simplify that of the 1-norm symmetric distributions to an expression of a finite sum. These forms of c.f.'s can be used to derive the probability density functions (p.d.f.'s) of linear combinations...