Comparing Fisher information in record values and their concomitants with random observations

In a sequence of bivariate random variables {(Xi, Yi ), i ≥ 1} from a continuous distribution with a real parameter θ, general comparison results between the amount of Fisher information about θ contained in the sequence of the first n records and their concomitants, and the desired information in an i.i.d. sample of size n from the parent distribution are established. Some relationships between reliability properties and the proposed criteria are obtained in situations in which the univariate counterpart of the underlying bivariate family belongs to location, scale or shape families. It is also shown that in some classes of bivariate families, the concerned information property is equivalent to that of its univariate counterpart. The proposed procedure is illustrated by considering several examples.

bivariate distribution; bivariate family; location and scale families; proportional hazard model; shape family; sufficient statistics