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 ( os) 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.

Based on the extensions of Morgenstern family (Huang and Bairamov extensions), the concomitants of different types of generalized order statistics (os) and dual generalized order statistics (d os) are obtained. Moreover, a unified approach to such models is derived. Information properties such as Shannon entropy and Kullback-Leibler divergence for Huang and Kotz extension are obtained.

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