Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Amit Ghosh and Chanchal Kundu ()
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Amit Ghosh: Rajiv Gandhi Institute of Petroleum Technology
Chanchal Kundu: Rajiv Gandhi Institute of Petroleum Technology

Statistical Papers, 2019, vol. 60, issue 6, No 18, 2225-2252

Abstract: Abstract In a recent paper, Kundu et al. (Metrika 79:335–356, 2016) study the notion of cumulative residual inaccuracy (CRI) and cumulative past inaccuracy (CPI) measures in univariate setup as a generalization of cumulative residual entropy and cumulative past entropy, respectively. Here we address the question of extending the definition of CRI (CPI) to bivariate setup and study their properties. We also prolong these measures to conditionally specified models of two components having possibly different ages or failed at different time instants called conditional CRI (CCRI) and conditional CPI (CCPI), respectively. We provide some bounds on using usual stochastic order and investigate several properties of CCRI (CCPI) including the effect of linear transformation. Moreover, we characterize some bivariate distributions.

Keywords: Cumulative residual (past) inaccuracy; Conditionally specified model; Conditional proportional (reversed) hazard rate; Usual stochastic order; Primary: 62B10; Secondary: 94A17; 62N05; 62H05 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-017-0917-5

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