G. Rajesh

A study of the effect of loss functions on the Bayes estimates of dynamic cumulative residual entropy for Pareto distribution under upper record values

Most of the data arising in reliability can be modelled by Pareto distribution. In the present paper, we proposed the Bayes estimation of dynamic cumulative residual entropy for the classical Pareto distribution under upper record values. This measure performs important roles in reliability and survival analysis to model and analyse the data. A class of informative and non-informative priors has been assumed to derive the corresponding posterior distributions. The Bayes estimators (BEs) and the associated posterior risks have been calculated under different symmetric and asymmetric loss functions. We demonstrate the use of the proposed Bayesian estimation procedure with the average July temperatures data of Neuenburg, Switzerland, during the period 1864–1993. The performance of the BEs has been evaluated and compared under a comprehensive simulation study. The purpose is to find out the combination of a loss function and a prior having the minimum Bayes risk and hence producing the best results.

Bivariate Geometric Vitality Function and Some Characterization Results

Abtsrcat In the present work we extends the definition of geometric vitality function, considered by Nair and Rajesh (2000) to the bivariate set up. We also look into the problem of characterizing some bivariate models using the functional form of the bivariate geometric vitality function.

Estimation of inaccuracy measure for censored dependent data

ABSTRACT In the present paper, we propose non parametric estimators for the inaccuracy measure for the lifetime distribution based on censored data. This measure plays important roles in reliability and survival analysis in connection with modeling and analysis of life time data. Asymptotic properties of the estimators are established under suitable regularity conditions. Monte Carlo simulation studies are carried out to compare the performance of the estimators using the mean-squared error. The methods are illustrated using a real data set.

Nonparametric Estimation of the Geometric Vitality Function

Recently, Nair and Rajesh (2000) proposed a measure to describe the failure pattern of components/devices in terms of the geometric mean of the residual life. This measure find applications in modeling life time data. In the present work we provide a nonparametric kernel-type estimator for the geometric vitality function, both in the case of complete and censored samples. The properties of the estimator, under certain regularity conditions, are studied. The performance of the estimator is compared with the empirical estimator using a real data set and simulation studies are carried out using the Monte Carlo method.

Bivariate Dynamic Weighted Failure Entropy of Order α

SYNOPTIC ABSTRACT Recently, Rohini et al. (2017) proposed a measure of uncertainty based on the distribution function called weighted failure entropy of order α. In this article, we extend the definition of weighted failure entropy of order α to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending weighted failure entropy of order α for conditionally specified models. Several properties are obtained for conditional distributions. Along with some characterization results, it is shown that the proposed measure uniquely determines the distribution function. Moreover, we also proposed an empirical estimator for the new measure.

Bayesian Estimation of Dynamic Cumulative Residual Entropy for Classical Pareto Distribution

SYNOPTIC ABSTRACT Dynamic cumulative residual entropy plays a significant role in reliability and survival analysis to model and analyze the data. This article presents Bayesian estimation of the dynamic cumulative residual entropy of the classical Pareto distribution using informative and non-informative priors. The Bayes estimators and their associated posterior risks are calculated under different symmetric and asymmetric loss functions. A numerical example is given to illustrate the results derived. Based on a Monte Carlo simulation study, comparisons are made between the proposed estimators. The objective of this article is to identify the combination of a loss function and a prior having the minimum Bayes risk in order to estimate efficiently the dynamic cumulative residual entropy of Pareto distribution.

Local linear estimation of residual entropy function of conditional distributions

Local linear estimators for the conditional residual entropy function in the case of complete and censored samples are proposed. The resulting estimators are shown to be consistent and asymptotically normally distributed under certain regularity conditions. The performance of the estimator is compared by using a real data set and simulation studies are carried out by using the Monte-Carlo method.