How much Fisher information is contained in record values and their concomitants in the presence of inter-record times?

It is shown that, although the distribution of inter-record time does not depend on the parent distribution, Fisher information increases when inter-record times are included. The general results concern different classes of bivariate distributions and propose a comparison study of the Fisher information. This study is done in situations in which the univariate counterpart of the underlying bivariate family belongs to a general continuous parametric family and its wellknown subclasses such as location-scale and shape families, exponential family and proportional (reversed) hazard model. We derived some explicit formulas for the additional information of record time given records and their concomitants (bivariate records) for some classes of bivariate distributions. Some common distributions are considered as examples for illustrations and are classified according to this criterion. A simulation study and a real data example from bivariate normal distribution are considered to study the relative efficiencies of estimator based on bivariate record values and inter-record times with respect to the corresponding estimator based on iid sample of the same size and bivariate records only

Concomitants of Upper Record Statistics for Bivariate Pseudo–Weibull Distribution

In this paper the Bivariate Pseudo–Weibull distribution has been defined as a compound distribution of two random variables to model the failure rate of component reliability. The distribution of r–th concomitant and joint distribution of r–th and s–th concomitant of record statistics of the resulting distribution have been derived. Single and product moments alongside the correlation coefficient have also been obtained. Recurrence relation for the single moments has also been obtained for the resulting distributions

Concomitants of Record Values From a General Farlie-Gumbel-Morgenstern Distribution

In this paper, we discuss the distributions of concomitants of record values arising from a polynomial-type single parameter extension of general Farlie-Gumbel-Morgenstern bivariate distribution. We derive the single and the product moments of concomitants of record values generally for any marginal distributions. The results obtained are applied to two-parameters exponential marginal distributions. In this case, we show that the maximal positive correlation between the two variables is approximately =423. Best linear unbiased estimators based on concomitants of record values of some parameters involved in the distribution are derived. Moreover, we obtain predictors of concomitants of record values by two methods. Finally a numerical illustration is presented to highlight the theoretical results obtained

On Stochastic Comparisons of Concomitants of Generalized Order Statistics

In this article, the problem of comparing concomitants of generalized order statistics (GOSs) in terms of different types of stochastic orders is considered. Some stochastic ordering results for compound random variables in the one-sample problems are recalled and extended. Analogous results are obtained in the two-sample setup. The derived results are used to compare concomitants of GOSs in both one-sample problems and two-sample problems. We also introduce some new joint stochastic orders (namely, the joint reversed hazard order and the joint convex order) and compare concomitants in terms of these orders

Inaccuracy measures for concomitants of generalized order statistics in Morgenstern family

In this paper, we obtain a measure of inaccuracy between rth concomitant of generalized order statistic and the parent random variable in Morgenstern family. Applications of this result are given for concomitants of order statistics and record values. We also study some results of cumulative past inaccuracy (CPI) between the distribution function of rth concomitant of order statistic (record value) and the distribution function of parent random variable. Finally, we discuss on a problem of estimating the CPI by means of the empirical CPI in concomitants of generalized order statistics

Multivariate order statistics via multivariate concomitants

AbstractLet X¯1,…,X¯n denote a set of n independent identically distributed k-dimensional absolutely continuous random variables. A general class of complete orderings of such random vectors is supplied by viewing them as concomitants of an auxiliary random variable. The resulting definitions of multivariate order statistics subsume and extend orderings that have been previously proposed such as norm ordering and N-conditional ordering. Analogous concepts of multivariate record values and multivariate generalized order statistics are also described