S. M. Sunoj

Dynamic cumulative residual Renyi's entropy

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannons 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 Renyis 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.

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannons measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them.

Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specified models and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order.

Some Properties of Weighted Distributions in the Context of Repairable Systems

ABSTRACT In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables.

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto II and beta distributions. Further, we generalize the identities for the Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in the context of lengthbiased models are also explored.

Form-invariant bivariate weighted models

In this paper the class of continuous bivariate distributions that has form-invariant weighted distribution with weight function [Formula: See Text] is identified. It is shown that the class includes some well known bivariate models. Bayesian inference on the parameters of the class is considered and it is shown that there exist natural conjugate priors for the parameters.

Quantile-based cumulative entropies

ABSTRACT It is well known that Shannon’s entropy plays an important role in the measurement of uncertainty of probability distributions. However, in certain situations Shannon entropy is not appropriate to measure the uncertainty and therefore an alternative measure has been introduced called cumulative residual entropy, based on the survival function (sf) instead of the probability density function (pdf) f(x) used in Shannon’s entropy. In the present paper, we introduce and study quantile versions of the cumulative entropy functions in the residual and past lifetimes. Unlike the cumulative entropies based on sf, the quantile-based cumulative entropy measures uniquely determine the underlying probability distribution.

Bivariate Weighted Distributions in the Context of Reliability Modelling

In this paper we consider the weighted conditional models and bivariate weighted models using different weight functions and examine its relationships in the context of reliability modelling. We also study the dependence nature of the bivariate weighted models using the local dependence function introduced by Holland and Wang (1987).

Quantile-based cumulative Kullback–Leibler divergence

ABSTRACT The paper introduces a quantile-based cumulative Kullback–Leibler divergence and study its various properties. Unlike the distribution function approach, the quantile-based measure possesses some unique properties. The quantile functions used in many applied works do not have any tractable distribution functions where the proposed measure is a useful tool to compute the distance between two random variables. Some useful bounds are obtained for quantile-based residual cumulative Kullback–Leibler divergence and quantile-based reliability measures. Characterization results based on the functional forms of quantile-based residual Kullback–Leibler divergence are obtained for some well-known life distributions, namely exponential, Pareto II and beta.

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.