Dynamic Cumulative Residual Entropy Research Articles

Dynamic cumulative residual entropy generating function and its properties

In this work, we study the properties of the cumulative residual entropy generating function (CREGF). We also discuss the non parametric estimation of CREGF. We introduce dynamic cumulative residual entropy generating function (DCREGF). It is shown that the DCREGF determines the distribution uniquely. We study some characterization results using the relationship between DCREGF, hazard rate, and mean residual life function. A new class of life distributions based on decreasing DCREGF is introduced. Finally, we develop a test for decreasing DCREGF and study its performance.

Bayesian and non-Bayesian estimation of dynamic cumulative residual Tsallis entropy for moment exponential distribution under progressive censored type II

Abstract The dynamic cumulative residual (DCR) entropy is a helpful randomness metric that may be used in survival analysis. A challenging issue in statistics and machine learning is the estimation of entropy measures. This article uses progressive censored type II (PCT-II) samples to estimate the DCR Tsallis entropy (DCRTE) for the moment exponential distribution. The non-Bayesian and Bayesian approaches are the recommended estimating strategies. We obtain the DCRTE Bayesian estimator using the gamma and uniform priors via symmetric and asymmetric (linear exponential and general entropy) loss functions (LoFs). The Metropolis–Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution. The accuracy of different estimates for various sample sizes, is implemented via Monte Carlo simulations. Generally, we note based on the simulation study that, in the majority of cases, the DCRTE Bayesian estimates under general entropy followed by linear exponential LoFs are preferable to the others. The accuracy measure of DCRTE Bayesian estimates using a gamma prior has smaller values than the others using a uniform prior. As sample sizes grow, the Bayesian estimates of the DCRTE are closer to the true value. Finally, analysis of the leukemia data confirmed the proposed estimators.

Bayesian Estimators of Dynamic Cumulative Residual Entropy for Pareto Type II Distribution

In this paper, Pareto type II distribution is used to propose Bayes estimator of dynamic cumulative residual entropy. To calculate posterior risks, various informative and non-informative priors are used. Using different loss functions, Bayes estimators and associated posterior risks for the distribution have been calculated. Numerical computation is carried out with the help of a real dataset. In the last, Monte Carlo Simulation study and Graphical analysis are also given along with the conclusion drawn.

Statistical inference of dependent competing risks from Marshall–Olkin bivariate Burr-XII distribution under complex censoring

Dealing with competing risks is an important problem in reliability analysis and attracts much attention from scholars. It is more practical to consider competing risks with dependent failure causes in reality. In this article, statistical inference of the Marshall–Olkin bivariate Burr-XII distribution under adaptive type-II progressive hybrid censoring is discussed to show the procedure of dependent competing risks analysis in the complex data structure. The maximum likelihood estimation and lognormal approximation confidence intervals of parameters are computed. The existence and uniqueness of solutions are proved with Cauchy-Schwarz inequality. The Bayesian method with Gamma-Dirichlet prior and Metropolis-Hastings algorithm are further considered to find satisfied estimation of parameters. In addition, dynamic cumulative residual entropy is derived to quantify the information uncertainty of data. We finally compare the performance of various methods by conducting a simulation study and real data analysis.

Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data.

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an -mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

On cumulative residual Renyi's entropy for double truncated distribution

Recently, a new class of uncertainty measure, namely the dynamic cumulative residual Renyi's entropy, has been introduced and studied in the literature. In parallel to that here, we have defined cumulative residual Renyi's entropy for a doubly truncated random variable called interval cumulative residual Renyi's entropy (ICRRE). Several properties, including the effect of monotone transformation, and bounds of ICRRE are discussed. Furthermore, it is shown that the proposed measure uniquely determines the distribution function and obtained characterizations of some well-known life distributions. Finally, we have proposed four nonparametric estimators of ICRRE and compared their performance by using the Monte-Carlo simulation study. A real-life data set is also illustrated based on the best-proposed estimator.

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution.

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

English

In this paper, we obtain lower bounds for the variance of a function of random variables in terms of measures of reliability and entropy. Also based on the obtained characterization via the lower bounds for the variance of a function of random variable X, we find a characterization of the weighted function corresponding to density function f(x), in terms of Chernoff-type inequalities. Subsequently, we obtain monotonic relationships between variance residual life and dynamic cumulative residual entropy and between variance past lifetime and dynamic cumulative past entropy. Moreover, we find lower bounds for the variance of functions of weighted random variables with specific weight functions applicable in reliability under suitable conditions.

Dynamic cumulative residual Rényi entropy for Lomax distribution: Bayesian and non-Bayesian methods

<abstract> An alternative measure of uncertainty related to residual lifetime function is the dynamic cumulative residual entropy which plays a significant role in reliability and survival analysis. This article deals with estimating dynamic cumulative residual Rényi entropy (DCRRE) for Lomax distribution using maximum likelihood and Bayesian methods of estimation. The maximum likelihood estimates and approximate confidence intervals of DCRRE are derived. Bayesian estimates and Bayesian credible intervals are derived based on gamma priors for the DCRRE under squared error, linear exponential (LINEX) and precautionary loss functions. The Metropolis-Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distributions. The Bayes estimates are compared through Monte Carlo simulations. Regarding simulation results, we observe that the maximum likelihood and Bayesian estimates of the DCRRE are decreasing function on time. Further, maximum likelihood and Bayesian estimates of the DCRRE perform well as the sample size increases. Bayesian estimate of the DCRRE under LINEX loss function is more convenient than the other estimates in the most of the situations. Real data set is analyzed for clarifying purposes. </abstract>

Bayesian inference of dynamic cumulative residual entropy from Pareto Ⅱ distribution with application to COVID-19

&lt;abstract&gt; &lt;p&gt;Dynamic cumulative residual entropy is a recent measure of uncertainty which plays a substantial role in reliability and survival studies. This article comes up with Bayesian estimation of the dynamic cumulative residual entropy of Pareto Ⅱ distribution in case of non-informative and informative priors. The Bayesian estimator and the corresponding credible interval are obtained under squared error, linear exponential (LINEX) and precautionary loss functions. The Metropolis-Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution. A simulation study is done to implement and compare the accuracy of considered estimates in terms of their relative absolute bias, estimated risk and the width of credible intervals. Regarding the outputs of simulation study, Bayesian estimate of dynamic cumulative residual entropy under LINEX loss function is preferable than the other estimates in most of situations. Further, the estimated risks of dynamic cumulative residual entropy decrease as the value of estimated entropy decreases. Eventually, inferential procedure developed in this paper is illustrated via a real data.&lt;/p&gt; &lt;/abstract&gt;

A quantile-based generalized dynamic cumulative measure of entropy

ABSTRACTThe cumulative residual entropy (CRE), introduced by Rao et al. (2004), is a new measure of uncertainty and viewed as a dynamic measure of uncertainty. Asadi and Zohrevand (2007) proposed a dynamic form of the CRE, namely dynamic CRE. Recently, Kumar and Taneja (2011) introduced a generalized dynamic CRE based on the Varma entropy introduced by Varma (1966) and called it dynamic CRE of order α and type β. In the present article, we introduce a quantile version of the dynamic CRE of order α and type β and study its properties. For this measure, we obtain some characterization results, aging classes properties, and stochastic comparisons.

Bayesian Estimation of Dynamic Cumulative Residual Entropy for Classical Pareto Distribution

SYNOPTIC ABSTRACTDynamic 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.

Characterization results based on dynamic Tsallis cumulative residual entropy

ABSTRACTIn this article, the concept of cumulative residual entropy (CRE) given by Rao et al. (2004) is extended to Tsallis entropy function and dynamic version, both residual and past of it. We study some properties and characterization results for these generalized measures. In addition, we provide some characterization results of the first-order statistic based on the Tsallis survival entropy.

BIVARIATE DYNAMIC CUMULATIVE RESIDUAL TSALLIS ENTROPY

Recently, Sati and Gupta (2015) proposed two measures of uncertainty based on non-extensive entropy, called the dynamic cumulative residual Tsallis entropy (DCRTE) and the empirical cumulative Tsallis entropy. In the present paper, we extend the definition of DCRTE into the bivariate setup and study its properties in the context of reliability theory. We also define a new class of life distributions based on bivariate DCRTE.

On Dynamic Cumulative Residual Entropy of Order Statistics

On Dynamic Cumulative Residual Entropy of Order Statistics

Discrete (Dynamic) Cumulative Residual Entropy in Bivariate case

Discrete (Dynamic) Cumulative Residual Entropy in Bivariate case

Bayes estimation of dynamic cumulative residual entropy for Pareto distribution under type-II right censored data

Information measures play a vital role in reliability modeling and survival analysis of life time data. In this article, we propose the Bayesian estimation of the dynamic cumulative residual entropy for the classical Pareto distribution using a type-II right censored data. Pareto distribution can be used to model many data arising from reliability studies. To derive the corresponding posterior distributions, we use a class of informative and non-informative priors. We derive the Bayes estimators and their associated posterior risks under different symmetric and asymmetric loss functions. We illustrate the application of the proposed Bayesian estimation procedure using the (Dyer, 1981) annual wage data. To demonstrate the closeness of the Bayes estimators with the true value of the parameters, we have carried out a simulation study. The main interest in this paper is to identify an appropriate combination of a loss function and a prior which minimizes the Bayesian posterior risk.

Testing exponentiality of the residual life, based on dynamic cumulative residual entropy

A new test statistic is developed for testing exponentiality of the remaining life of a system. Asymptotic properties of the test statistic are discussed. Then, Monte Carlo simulation is used to compare the power of the proposed test with that of an existing test.

On generalized dynamic cumulative past entropy measure

ABSTRACTRecently, the concept of dynamic cumulative residual entropy and its generalizations has gained much attention among researchers. In this work, a new generalized dynamic cumulative measure in the past lifetime is proposed. Further, some characterization results connecting this new generalized dynamic entropy measure and other reversed measures are obtained.

On the dynamic cumulative residual quantile entropy ordering

A new stochastic order called dynamic cumulative residual quantile entropy (DCRQE) order is established. Some characterizations of the new order are investigated. Closure and reversed closure properties of the DCRQE order are obtained. Applications of the DCRQE ordering in characterizing the proportional hazard rate model and the k-record values model are considered.