Limit Distributions Of Order Statistics Research Articles

Limit distributions of order statistics with random indices in a stationary Gaussian sequence

ABSTRACTIn this article, we study the limit distributions of the extreme, intermediate, and central order statistics (os) of a stationary Gaussian sequence under equi-correlated setup. When the random sample size is assumed to converge weakly and to be independent of the basic variables, the sufficient (and in some cases the necessary) conditions for the convergence are derived. Finally, we show that the obtained result for the maximum os, with random sample size, is also applicable in the case of the non constant correlation case.

Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

On distribution functions with completely monotone derivative

A necessary and sufficient condition for the existence of the mean of distributions with completely monotone derivative is given. Distributions with completely monotone hazard rate are identified. Limit distributions of order statistics in a sample from F( x) which has completely monotone derivative is discussed.

Limit Distributions for Order Statistics. II

Limit Distributions for Order Statistics. II

Limit Distributions for Order Statistics. I

Limit Distributions for Order Statistics. I

On Limit Distributions for Order Statistics

The limit distribution of the k-th order statistic in a sample of size n is considered when k increases as $n^\alpha $, $0 < \alpha < 1$, namely when the condition (7) on k is satisfied. The possible types of limit distributions and their domains of attraction are derived.