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On some dynamic generalized information measures for bivariate lifetimes

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  • Chanchal Kundu
  • Amit Ghosh

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.

Suggested Citation

  • Chanchal Kundu & Amit Ghosh, 2018. "On some dynamic generalized information measures for bivariate lifetimes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(22), pages 5497-5513, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:22:p:5497-5513
    DOI: 10.1080/03610926.2017.1395051
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