Applications of Mathematics, Vol. 63, No. 2, pp. 167-193, 2018
On generalized conditional cumulative past inaccuracy measure
Amit Ghosh, Chanchal Kundu
Received June 26, 2017. First published April 9, 2018.
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.
Keywords: cumulative past inaccuracy; marginal and conditional past lifetimes; conditional proportional reversed hazard rate model; usual stochastic order
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Affiliations: Amit Ghosh, Chanchal Kundu (corresponding author), Department of Mathematics, Rajiv Gandhi Institute of Petroleum Technology, Jais 229 304, Uttar Pradesh, India, e-mail: ckundu@rgipt.ac.in, chanchal_kundu@yahoo.com
