A probelm of J. Neyman (in Classical and Contagious Discrete Distributions (G. P. Patil, Ed.), 1965, pp. 4-14) regarding a characterization of positive and negative multinomial distributions is studied in this paper. Some properties of multivariate power series distributions in general which...

Let X[alpha] = (X1[alpha],..., Xp[alpha]), 1 <= [alpha] <= N[nu], [nu] >= 1 be N[nu] independent observations from a density function f(x) where x [set membership, variant] Rp, the p-dimensional real space. Let R[nu]j[alpha] denote the rank of Xj[alpha] in the ordered array of Xj1 ,..., XjN[nu]; 1 <= j <= p and consider the multivariate rank order statistics where the constants, c[nu][alpha], 1 <= [alpha] <= N[nu] satisfy the Noether condition and the scores, a[nu]j([alpha]), 1 <= j <= p, 1 <= [alpha] <= N[nu] converge as [nu] --> [infinity], for each j,...</=></=>

In this paper, the author gives a review of the literature on complex multivariate distributions. Some new results on these distributions are also given. Finally, the author discusses the applications of the complex multivariate distributions in the area of the inference on multiple time series.

We investigate the structure of distributions for matrices which can be embedded in arbitrarily large matrices whose distributions have properties of invariance under orthogonal rotations.

This paper considers three types of problems: (i) the problem of independence of two sets, (ii) the problem of sphericity of the covariance matrix [Sigma], and (iii) the problem of intraclass model for the covariance matrix [Sigma], when the column vectors of X are independently distributed as...

If X1, ..., Xn are independent Rd-valued random vectors with common distribution function F, and if Fn is the empirical distribution function for X1, ..., Xn, then, among other things, it is shown that P{supx | Fn(x) | [greater-or-equal, slanted] [epsilon]} [less-than-or-equals, slant]...

Chung's general form of the law of the iterated logarithm for the Kolmogorov statistic (Trans. Amer. Math. Soc. 67, 36-50) is generalized to a wide class of statistics including some important Renyi statistics.

In the Gaussian channel Y(t) = [Phi](t) + X(t) = message + noise, where [Phi](t) and X(t) are mutually independent, the information I(Y, [Phi]) is evaluated. One of the results is that I(Y, [Phi]) [infinity] if and only if [Phi] [epsilon] (X) = the reproducing kernel Hilbert space for X(·)....

This expository paper gives a survey of statistical problems arising in two important and widely used scientific methods of dating archaeological deposits, namely tree-ring-calibrated radiocarbon dates and seriation.

It is shown that--under appropriate regularity conditions--the conditional distribution of the first p components of a normalized sum of i.i.d. m-dimensional random vectors, given the complementary subvector, admits a Chebyshev-Cramér asymptotic expansion of order o(n-(s-2)/2), uniformly over...