On some dynamic generalized measures of information for conditionally specified models in past life

ABSTRACT

In the present work, we consider the extension of generalized Kullback–Leibler divergence measure of order $(\alpha ,\beta )$ proposed by Kundu [Generalized measures of information for truncated random variables. Metrika. 2015;78:415–435] and Kerridge inaccuracy measure of order α defined in Nath [Inaccuracy and coding theory. Metrika. 1968;13:123–135] to higher dimensions with focus on past lifetimes. These measures are extended to conditionally specified models of two components failed at different time instants. We provide some bounds using likelihood ratio order and investigate several properties, including monotonicity, of these measures for conditionally specified models. Moreover, we study the effect of (increasing) monotone transformation on these generalized conditional measures.

KEYWORDS:

• Conditionally specified model
• conditional proportional reversed hazard rate
• Kullback–Leibler divergence measure
• Kerridge's inaccuracy measure
• likelihood ratio order

AMS 2010 CLASSIFICATIONS:

• Primary: 62B10
• Secondary: 62N05
• 62H05

Acknowledgments

We are thankful to the Editor-in-Chief of the journal and anonymous reviewers for their valuable comments and suggestions which have considerably improved the content of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The financial support (Ref. No. SR/FTP/MS-016/2012) rendered by the Science and Engineering Research Board, Government of India is acknowledged with thanks by C. Kundu for carrying out this research work.