A new family of continuous multivariate distributions is introduced, generalizing the canonical form of the multivariate normal distribution. The well-known univariate version of this family, as developed by Box, Tiao and Lund, among others, has proven a valuable tool in Bayesian analysis and...

The class of random processes with spectral multiplicity equal to one is shown to be dinse in various broader classes of processes with finite energy under the norm of L2([Omega] - T; dp - dt). In some special cases constructive procedures for establishing the denseness are outlined. The...

The asymptotic distributions of the elementary symmetric functions (esf's) of the characteristic roots of a noncentral multivariate beta matrix and of the generalized correlation matrix (noncentral under the assumption of linearity) are derived.

Fredholm's integral equation theory and Mittag-Leffler expansion is used for getting characteristic functions and three ways of expressing the Bernoulli numbers.

This paper is devoted to the theory and application of multidimensional stable distributions. Properties of these laws are developed and explicit algebraic representations are given in terms of characteristic functions. Symmetric and asymmetric laws and their properties are studied separately. A...

The condition on the offspring distribution in the critical multitype Bienaymé-Galton-Watson process without variance, which was previously shown to be sufficient for the existence of the analogue of the exponential limit law, is now shown also to be necessary. This completely extends previous...

It is known that if the statistic Y = [Sigma]j=1n(Xj + aj)2 is drawn from a population which is distributed N(0, [sigma]) then the distribution of Y depends on only. Kagan and Shalaevski [2] have shown that if the random variables X1, X2, ..., Xn are independent and identically distributed and...

A method is given for testing the independence of variates in an infinitely divisible random vector and for testing the independence of several subsets of the variates. Applications to stochastic processes are indicated.

Optimality of estimators of a vector parameter in terms of the probability of the estimators being contained in suitable region(s) around the parameter point is defined. Conditions under which optimal estimators in the usual senses are also optimal in the above sense are investigated.