On generalized conditional cumulative past inaccuracy measure

Amit Ghosh; Chanchal Kundu

Applications of Mathematics (2018)

  • Volume: 63, Issue: 2, page 167-193
  • ISSN: 0862-7940

Abstract

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The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI are discussed. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Finally, the role of GCCPI in reliability modeling has also been investigated for a real-life problem.

How to cite

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Ghosh, Amit, and Kundu, Chanchal. "On generalized conditional cumulative past inaccuracy measure." Applications of Mathematics 63.2 (2018): 167-193. <http://eudml.org/doc/294335>.

@article{Ghosh2018,
abstract = {The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order $\alpha $ and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI are discussed. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Finally, the role of GCCPI in reliability modeling has also been investigated for a real-life problem.},
author = {Ghosh, Amit, Kundu, Chanchal},
journal = {Applications of Mathematics},
keywords = {cumulative past inaccuracy; marginal and conditional past lifetimes; conditional proportional reversed hazard rate model; usual stochastic order},
language = {eng},
number = {2},
pages = {167-193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On generalized conditional cumulative past inaccuracy measure},
url = {http://eudml.org/doc/294335},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Ghosh, Amit
AU - Kundu, Chanchal
TI - On generalized conditional cumulative past inaccuracy measure
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 167
EP - 193
AB - The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order $\alpha $ and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI are discussed. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Finally, the role of GCCPI in reliability modeling has also been investigated for a real-life problem.
LA - eng
KW - cumulative past inaccuracy; marginal and conditional past lifetimes; conditional proportional reversed hazard rate model; usual stochastic order
UR - http://eudml.org/doc/294335
ER -

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