Papers by E.i.abdul Sathar
Ricerche di Matematica/Ricerche di matematica, Apr 30, 2024
Journal of the Indian Society for Probability and Statistics, Feb 16, 2024
Japanese Journal of Statistics and Data Science, Dec 13, 2023
International journal of system assurance engineering and management, Feb 4, 2024
Communications in Statistics - Simulation and Computation, Jun 23, 2023
Statistics & Probability Letters, Nov 1, 2019
We describe a method for quantifying the lack of fit in a proposed family of distributions. The m... more We describe a method for quantifying the lack of fit in a proposed family of distributions. The method involves estimating the posterior distribution of the Kullback-Leibler information between the true distribution generating the data and the proposed family. We include an implementation for discrete data involving Dirichlet Processes, for continuous data involving Dirichlet Process Mixtures, and for regression data involving a common "perturbation" distribution also estimated by a Dirichlet Process Mixture. We examine the effectiveness of the method through simulation. We also show that, for independent, identically distributed discrete data, the posterior distribution from a Dirichlet Process provides a consistent estimate of the KL information. Because the entire posterior distribution is computed, one can readily acquire interval estimates of the distance without resorting to asymptotics.
Journal of the Indian Society for Probability and Statistics
Mathematical Methods of Statistics
Sri Lankan Journal of Applied Statistics, 2021
This paper estimates the power function distribution parameters and predicts the future record va... more This paper estimates the power function distribution parameters and predicts the future record values when samples are available only in the form of upper record values. We considered the maximum likelihood and Bayesian techniques for the estimation. We also construct asymptotic, bootstrap, and HPD confidence intervals for the unknown parameters. Bayes estimators are derived using the squared error loss function, entropy loss function, and Linex loss function using the Lindley approximation and importance sampling procedures. Finally, we conduct a simulation study to compare all the proposed estimation methods and analyse a real data set for illustration purposes.
Metrika, 2020
In this article, we propose geometric vitality function introduced by Nair and Rajesh (IAPQR Tran... more In this article, we propose geometric vitality function introduced by Nair and Rajesh (IAPQR Trans 25(1):1-8, 2000) for the past lifetime of a random variable. This measure plays a vital role in analysing different characteristics of a system/component when it fails in the interval (0, t). The monotonic behaviour and some ordering properties in terms of the proposed measure were studied under certain conditions. Similar properties of the proposed measure were analysed for order statistics as well. Further, bounds were obtained for the past geometric vitality function of order statistics. Apart from this, characterizations of some lifetime probability distributions with respect to order statistics were also discussed.
International Journal of Reliability, Quality and Safety Engineering
This paper introduces the concept of cumulative extropy in a past lifetime using the quantile fun... more This paper introduces the concept of cumulative extropy in a past lifetime using the quantile function and establishes its monotone and ordering properties. It also demonstrates an application of this new measure for various distributions commonly used in lifetime data analysis, and provides a nonparametric estimator for the quantile-based cumulative extropy in a past lifetime.
Statistics & Probability Letters
Statistics & Probability Letters, 2018
Abstract Recently, extropy was defined as an alternative measure of uncertainity to that of entro... more Abstract Recently, extropy was defined as an alternative measure of uncertainity to that of entropy. But in measuring uncertainity about remaining lifetime of a component entropy was not much useful and hence residual entropy was formulated. Analogous to residual entropy, residual extropy was defined and used to study about the uncertainity of remaining life of a unit. In this paper, we defined the residual extropy of k -records arising from any continuous distribution in terms of residual extropy of k -records arising from uniform distribution. We also obtain lower bound for residual extropy of upper and lower k -records arising from any continuous probability distribution. Further, we discuss the monotone property of residual extropy of both upper and lower k -records.
Journal of the Indian Society for Probability and Statistics
Statistica, 2019
In this paper, we proposed MLE and Bayes estimators of parameters and DCPE for the two parameter ... more In this paper, we proposed MLE and Bayes estimators of parameters and DCPE for the two parameter power function distribution. Bayes estimators under different loss functions are obtained using Lindley approximation method and important sampling procedures. A real life data set and a Monte Carlo simulation are used to study the performance of the estimators derived in the article.
Journal of the Iranian Statistical Society, 2020
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Papers by E.i.abdul Sathar