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Stress-strength based on $$m$$-generalized order statistics and concomitant for dependent families. (English) Zbl 07088750
Summary: The stress-strength model is proposed based on the $$m$$-generalized order statistics and the corresponding concomitant. For the dependency between $$m$$-generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional reversed hazard functions as marginal functions. Based on the order statistics and record values, two estimators of stress-strength are presented using a procedure similar to the inference functions for margins. Finally, a simulation study is carried out which shows the good performance of the proposed estimators for a finite sample.

##### MSC:
 62G30 Order statistics; empirical distribution functions 62N05 Reliability and life testing
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