In this paper a multivariate failure rate representation based on Cox's conditional failure rate is introduced, characterizations of the Freund-Block and the Marshall-Olkin multivariate exponential distributions are obtained, and generalizations of the Block-Basu and the Friday-Patil bivariate...

In this paper a method for obtaining a.s. consistency in nonparametric estimation is presented which only requires the handling of covariances. This method is applied to kernel density estimation and kernel and nearest neighbour regression estimation. It leads to conditions for a.s. consistency...

LetX1, ..., Xnbe i.i.d. randomd-vectors,d[greater-or-equal, slanted]1, with sample meanXand sample covariance matrixS. For testing the hypothesisHdthat the law ofX1is some nondegenerate normal distribution, there is a whole class of practicable affine invariant and universally consistent...

The copula for a bivariate distribution functionH(x, y) with marginal distribution functionsF(x) andG(y) is the functionCdefined byH(x, y)=C(F(x), G(y)).Cis called Archimedean ifC(u, v)=[phi]-1([phi](u)+[phi](v)), where[phi]is a convex decreasing continuous function on (0, 1]...

In this paper, we take the characteristic function approach to goodness-of-fit tests. It has several advantages over existing methods: First, unlike the popular comparison density function approach suggested in Parzen (1979), our approach is applicable to both univariate and multivariate data;...

In this paper some characterization results ofLp-norm spherical distributions are obtained. It is proved that ifX=(X1, ..., Xn)' has aLp-norm spherical distribution having certain independence properties, thenX1, X2, ..., Xnmust be i.i.d. with p.d.f.p(x)[is proportional to]e-xp/c....

Asymptotic chi-squared test statistics for testing the equality of moment vectors are developed. The test statistics proposed are generalized Wald test statistics that specialize for different settings by inserting an appropriate asymptotic variance matrix of sample moments. Scaled test...

The supermodular and the symmetric supermodular stochastic orders have been cursorily studied in previous literature. In this paper we study these orders more thoroughly. First we obtain some basic properties of these orders. We then apply these results in order to obtain comparisons of random...

A conjecture concerning the Cramér-Wold device is answered in the negative by giving a Fourier-free, probabilistic proof using only elementary techniques. It is also shown how a geometric idea allows one to interpret the Cramér-Wold device as a special case of a more general concept.

The paper gives sufficient conditions for domains of attraction of multivariate extreme value distributions. Under the assumption of absolute continuity of a multivariate distribution, the criteria enable one to examine, by using limits of some rescaled conditional densities, whether the...