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One of the most efficient and robust methods in estimation is to find the Fisher information matrix (FIM). In this paper, the FIM concerning order statistics (OSs) and their concomitants about the shape-parameter vector of Cambanis bivariate distribution is derived. This method contains information conveyed by singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution. In addition, we obtain and study the Fisher information (FI) about the mean and shape parameters in the concomitants of OSs for this bivariate distribution based on exponential and power function distributions. Finally, the information entropy of Shannon in the OSs and their concomitants based on the Cambanis distribution is studied. Some numerical computations were performed on the FI which lend support to the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we study the concomitants of m-generalized order statistics (m-GOS) from iterated Farlie–Gumbel–Morgenstern bivariate distributions, denoted by IFGM (λ , η) , as an extension of several recent papers. Furthermore, the joint distribution of m-GOS of concomitants for this family are studied. Some useful recurrence relations between moments of concomitants are obtained. The generalized exponential distribution is taken a typical case of the possible marginals of the IFGM (λ , η). Finally, the asymptotic behavior of the concomitant's rank for the model ordinary order statistics is studied. [ABSTRACT FROM AUTHOR]

By applying the cumulative hazard transformation, nonparametric prediction, inner and outer intervals based on generalized order statistics (GOSs) are obtained and their exact coverage probabilities are determined. The predictive intervals are accomplished based on informative sample of fixed, as well as random, number of GOSs from a continuous cumulative distribution function (CDF) F. When the sample size is random variable (RV), it is assumed to be positive integer and independent of both informative and future samples. Simulation study and numerical computations are conducted for illustrative purposes. [ABSTRACT FROM AUTHOR]

We study the limit distributions of upper and lower record values of a stationary Gaussian sequence (SGS) under an equi-correlated set up, when the random sample size is assumed to converge weakly and independent of the basic variables. Moreover, the class of limit distribution functions (df's) of joint upper and lower record values of a SGS with random indices are fully characterized. As an application of this result, the sufficient conditions for the weak convergence of record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product with random indices are obtained. Moreover, the classes of the non degenerate limit df's of these statistics are derived. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of general sequence of extreme, intermediate and central generalized-order statistics (gos), as well as dual generalized-order statistics (dgos), which are connected asymptotically with some regularly varying functions. Moreover, the limit distribution functions of gos, as well as dgos, with random indices, are obtained under general conditions. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions for the weak convergence of the generalized range, midrange, extremal quotient, and extremal product are obtained. The classes of possible non degenerate limit distribution functions of these simple statistics are characterized. Comparison study between these statistics with some examples for the most important distribution functions are given. [ABSTRACT FROM PUBLISHER]

The Marshall and Olkin (1997) parametrization operation is given by [image omitted] where F1 is a given distribution function and α > 0, [image omitted] = 1 - α. In this article, we show that both Fα = Pα(F1) and the generating distribution F1 belong to the same domain of maximal (minimal) (upper record value) (lower record value) attraction. Moreover, it is shown that the weak convergence of any non extreme order statistic (order statistic with variable rank) based on F1, under given normalizing constants, to a non degenerate limit type implies that the same non extreme order statistic based on the family Fα = Pα(F1), α≠1, under the same normalizing constants, does not converge to any non degenerate distribution and vice versa. [ABSTRACT FROM AUTHOR]

Based on the notion of the associated copula for order statistics (os's) and the L∞-distance, we derive a symmetric nonparametric measure of asymptotic dependence between the os's. This measure yields a nonparametric criterion of asymptotic dependence between os's under general normalization, such as power normalization. [ABSTRACT FROM AUTHOR]

In this article, by using the dropping argument, a general recurrence relation satisfied by the joint cumulative distribution functions of order statistics from any arbitrary bivariate distribution function is established. This recurrence relation is the first bivariate version of the basic triangle rule for order statistics arisen from univariate distribution function. Finally, this relation is extended to the trivariate case. These lead to similar identities for product moments (of any order) of order statistics. [ABSTRACT FROM AUTHOR]

This work gives a new representation of the distribution and expected value of the concomitant rank of order statistics. An advantage of this representation is its ability to extend without any complexity to the multivariate case. Moreover, it gives a new direct approach to compute an approximate formula for the distribution and expected value of the concomitant rank of order statistics. Finally, an upper bound is derived for the confidence level of the tolerance region of the original bivariate (resp., multivariate) d.f., from which the sample is drawn. [ABSTRACT FROM AUTHOR]