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Let be a multivariate normal random vector. We derive explicit expressions for the cumulative distribution function, probability density function and the moments of. Each expression involves single infinite sums of known special functions. Computational issues like accuracy, convergence, time and simulations are investigated. [ABSTRACT FROM AUTHOR]

For a type of strongly dependent isotropic Gaussian random fields introduced by Mittal (1976), the joint limiting distribution of the maximum and the sum for the Gaussian random fields is derived. The asymptotic relation between the maximum and sum of the continuous time strongly dependent isotropic Gaussian random fields and the maximum and sum of this fields sampled at discrete time points is also obtained. [ABSTRACT FROM AUTHOR]

Extreme value theory for discrete observations is very much underdeveloped. Here, we derive exact expressions for the cumulative distribution function ofMn, the maximum of a sequence ofndiscrete observations from a moving average of order one. A solution appropriate for largentakes the formwhere {νjx} are the eigenvalues of a certain matrix, andIdepends on the number of possible values of the underlying random variables. [ABSTRACT FROM AUTHOR]

In this article, we investigate the tail propertiesof the generalized Maxwell distribution and gain an asymptoticbehavior of its Mills-type ratio. Meanwhile, we show two applications. The first application thinks about the asymptotic property of the ratio of density functions and the ratio of the tails of the generalized Maxwell and classical Maxwell distributions. Another application obtains the asymptotic distribution of the partial maximum of an independent and identically distributed sequence from the distribution. [ABSTRACT FROM PUBLISHER]

Denote Mn the largest of n independent STSD variables. This article shows the rate of convergence of (Mn - bn)/an to the extreme value distribution exp (-e-x) which is characterized by the supremum metric. [ABSTRACT FROM AUTHOR]

We establish best upper bounds on the expected differences of records and sample maxima, and kth records and kth maxima based on sequences of independent random variables with identical continuous distribution and finite variance. The bounds are expressed in terms of the standard deviation units of the parent distribution. We also provide conditions for attaining the bounds. [ABSTRACT FROM AUTHOR]

We discuss some problems connected with the role of record values and maximal values generated by sequences of random variables X1, X2,..., Xn in the process of the growth of sums X1 +···+ Xn, n = 1, 2,.... [ABSTRACT FROM AUTHOR]

Cohen and Sackrowitz (1989) derive a uniformly minimum variance conditionally unbiased estimator (UMVCUE) for the mean of a selected population for the univariate normal case with variance known and unknown as well as for the gamma case in a two-stage design. We extend this methodology to the bivariate normal case where the covariance matrix is assumed to be known. The population with the largest sample mean of the first dimension is selected for additional observations in a second stage. The goal of the analysis is to find an unbiased estimate of the mean of the second dimension with all of the data. [ABSTRACT FROM AUTHOR]