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

Abstract

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.