Stress-strength based on m-generalized order statistics and concomitant for dependent families

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 stressstrength 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.