Applications of Mathematics, Vol. 64, No. 4, pp. 437-467, 2019


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

Filippo Domma, Abbas Eftekharian, Mostafa Razmkhah

Received October 16, 2018.   Published online June 21, 2019.

Abstract:  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.
Keywords:  copula function; Dagum distribution; generalized order statistics; Farlie-Gumbel-Morgenstern distribution; proportional reversed hazard family; record values
Classification MSC:  62G30, 62N05


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Affiliations:   Filippo Domma, Department of Economics, Statistics and Finance, University of Calabria, Via Pietro Bucci, Cubo 0C, 87036 Arcavacata di Rende (CS)-Italy; Abbas Eftekharian (corresponding author), Department of Statistics, Faculty of Science, University of Hormozgan, P.O. Box 3995, Bandar Abbas, Iran, e-mail: eftekharian@hormozgan.ac.ir; Mostafa Razmkhah, Department of Statistics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran


 
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