Frailty models have been developed for the analysis of bivariate survival data. The notion of shared frailty in these models, however, is different from the notion of individual frailty in demographic models. Shared frailty models have important shortcomings. We develop a new model of bivariate survival based on the notion of correlated individual frailty. We analyze the properties of this model and suggest a new approach to the analysis of bivariate data that does not require a parametric specification—but permits estimation—of the form of the hazard function for individuals. We empirically demonstrate the advantages of the model in the statistical analysis of bivariate data.

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Correlated individual frailty: an advantageous approach to survival analysis of bivariate data.

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models.

Dynamic cumulative residual Renyi's entropy

We consider a bivariate Pareto distribution, as a generalization of the Lindley-Singpurwalla model, by incorporating the influence of the operating conditions on a two-component dependent system. The properties of the model and its applications to reliability analysis are discussed. © 1993 John Wiley & Sons, Inc.

A bivariate pareto model and its applications to reliability

An overview is presented of some theoretical results concerning the mean residual life function used in reliability theory. An extension of the concept to the bivariate case is introduced, and the relationship between the reliability and mean residual life function is derived. The properties of the function and conditions for asymptotic exponentiality of component life lengths are discussed. >

Bivariate mean residual life

Bivariate extension of dynamic cumulative residual entropy

In this article a characterisation of the Gumbel's Bivariate Exponential Distribution is established on the basis of the properties of the conditional expectation of the component variables. The characterising property is proposed as the definition of lack of memory in the bivariate case.

N. U. Nair

Papers

A Characterization of the Bivariate Exponential Distribution