On generalized conditional cumulative residual inaccuracy measure

Abstract

Recently, the notion of cumulative residual Rényi’s entropy has been proposed in the literature as a measure of information that parallels Rényi’s entropy. Motivated by this, here we introduce a generalized measure of it, namely cumulative residual inaccuracy of order α. We study the proposed measure for conditionally specified models of two components having possibly different ages called generalized conditional cumulative residual inaccuracy measure. Several properties of generalized conditional cumulative residual inaccuracy measure including the effect of monotone transformation are investigated. Further, we provide some bounds on using the usual stochastic order and characterize some bivariate distributions using the concept of conditional proportional hazard rate model.

Keywords:

• Cumulative residual inaccuracy
• conditional proportional hazard rate model
• conditional survival and conditionally specified models
• the usual stochastic order

AMS 2010 CLASSIFICATIONS:

• Primary 62B10
• Secondary 94A17
• 62N05
• 62H05

Acknowledgments

The authors sincerely thank the anonymous reviewer for constructive comments and suggestions which have considerably improved the content of the paper.

Additional information

Funding

The financial support (Ref. No. 2/48(4)/2015/NBHM(R.P.)/R&D II/14130) rendered by the NBHM, Department of Atomic Energy, Government of India is acknowledged with thanks by C. Kundu.