On some dynamic generalized information measures for bivariate lifetimes

ABSTRACT

Several generalizations to the concept of Kullback-Leibler divergence measure and Kerridge inaccuracy measure are available in the literature. In a recent paper Kundu (Metrika, 78:415–435, 2015) considered a generalized K-L divergence measure of order (α, β). Nath (Metrika, 13:123–135, 1968) has also proposed generalized inaccuracy measure of order α. Here we address the question of extending these measures to higher dimensions with reference to residual lifetimes. In the present work, the generalized divergence and inaccuracy measures are extended for conditional lifetimes of two components having possibly different ages. Several properties, including monotonicity, and bounds of these measures are obtained for conditional random variables. Moreover, we study the effect of (increasing) monotone transformation on these generalized measures.

KEYWORDS:

• Conditional random variable
• Conditional proportional hazard rate
• Kerridge's inaccuracy measure
• Kullback-Leibler divergence measure
• Likelihood ratio order.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62B10
• Secondary 62N05, 62H05

Acknowledgements

The authors thank the anonymous reviewers for their 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.