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

Filippo Domma; Abbas Eftekharian; Mostafa Razmkhah

Applications of Mathematics (2019)

  • Volume: 64, Issue: 4, page 437-467
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Domma, Filippo, Eftekharian, Abbas, and Razmkhah, Mostafa. "Stress-strength based on $m$-generalized order statistics and concomitant for dependent families." Applications of Mathematics 64.4 (2019): 437-467. <http://eudml.org/doc/294787>.

@article{Domma2019,
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.},
author = {Domma, Filippo, Eftekharian, Abbas, Razmkhah, Mostafa},
journal = {Applications of Mathematics},
keywords = {copula function; Dagum distribution; generalized order statistics; Farlie-Gumbel-Morgenstern distribution; proportional reversed hazard family; record values},
language = {eng},
number = {4},
pages = {437-467},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stress-strength based on $m$-generalized order statistics and concomitant for dependent families},
url = {http://eudml.org/doc/294787},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Domma, Filippo
AU - Eftekharian, Abbas
AU - Razmkhah, Mostafa
TI - Stress-strength based on $m$-generalized order statistics and concomitant for dependent families
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 437
EP - 467
AB - 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.
LA - eng
KW - copula function; Dagum distribution; generalized order statistics; Farlie-Gumbel-Morgenstern distribution; proportional reversed hazard family; record values
UR - http://eudml.org/doc/294787
ER -

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