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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.