A measure of inaccuracy in concomitants of ordered random variables under Farlie-Gumbel-Morgenstern family

Abstract

In communication theory, for possible outcomes of an experiment, we have two basic problems for the statement of the experimenter: we may not have enough information (vague statement) or some of the information may be incorrect, which make inaccurate in either or both of these situations. In this article, a measure of inaccuracy and its residual between distributions of concomitants of generalized order statistics (1os) and parent random variable are extended. Results of inaccuracy for family distributions and stochastic comparisons are obtained. Furthermore, some properties of the proposed measure are discussed. The unique characterization of the distribution function of parent random variable by the inaccuracy is shown.