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Keywords:
copula function; Dagum distribution; generalized order statistics; Farlie-Gumbel-Morgenstern distribution; proportional reversed hazard family; record values
copula function; Dagum distribution; generalized order statistics; Farlie-Gumbel-Morgenstern distribution; proportional reversed hazard family; record values
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.
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