General Entropy Loss Function Research Articles

Classical and Bayesian Inference for an Extension of the Exponential Distribution under Progressive Type-II Censored Data with Binomial Removals

Maximum likelihood and Bayes estimators of the unknown parameters of an extension of the exponential (EE) distribution have been obtained for Progressive Type-II Censored data with Binomial removals. Markov Chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the parameters of interest. The General Entropy Loss Function (GELF) and Squared Error Loss Function (SELF) have been considered for obtaining the Bayes estimators. Comparisons are made between Bayesian and Maximum likelihood estimators (MLEs) via Monte Carlo simulation. An example is discussed to illustrate its applicability.

Bayes estimation of change point in the count data model: a Particular case of Discrete Burr Type III Distribution

A sequence of independent count data X1, X2..., Xm, Xm+1,...., Xnwhere observations from a particular case of discrete Burr family-type III distribution with distribution function F1(t) at time t later it was found that there was change in the system at some point of time m and it is a reflected in the sequence Xmby change in distribution function F2(t) at time t. The Bayes estimates of change point and parameters of Particular case of Bur Type III Distribution are derived under Linex and General Entropy loss functions.

Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study

In this article we consider statistical inferences about the unknown parameters of the Inverse Weibull distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures we propose using the maximum likelihood; the least squares methods and the approximate maximum likelihood estimators. The Bayes estimators are obtained based on both the symmetric and asymmetric (Linex, General Entropy and Precautionary) loss functions. There are no explicit forms for the Bayes estimators, therefore, we propose Lindley׳s approximation method to compute the Bayes estimators. A comparison between these estimators is provided by using extensive simulation and three criteria, namely, Bias, mean squared error and Pitman nearness (PN) probability. It is concluded that the approximate Bayes estimators outperform the classical estimators most of the time. Real life data example is provided to illustrate our proposed estimators.

Double Stage Shrinkage Estimation of the Reliability Function of the Proportional Hazard Family of Distribution Function under Different Loss Functions Using Progressive Type II Censored Sample

In this paper we propose two double stage shrinkage estimators of the reliability function of the proportional hazard family of distribution functions, using progressive type II censored sample. The risk functions and relative risk functions of the suggested estimators are derived under symmetric and asymmetric loss functions, viz., the squared error loss function and the general entropy loss function. The results show that the proposed estimators have better performance than a classical estimator in terms relative risk.

Bayesian Inference Based on the Interval Grouped Data from the Weibull Model with Application

In this paper, based on the interval grouped data, Bayesian approach is used to obtain estimator for the Weibull scale parameter and some lifetime such as the reliability and hazard functions. The estimation procedures have been developed and modified under squared error loss function (SELF) and general entropy loss function (GELF). The estimators are derived using the inverted gamma conjugate prior. Credible intervals and high posterior density (HPD) credible intervals are also obtained. Prediction for the future number of failures in the corresponding intervals is presented. Finally, real life example is applied to illustrate the performance of the estimation procedures.

Parametric inference of non-informative censored time-to-event data

Random or non-informative censoring is when each subject has a censoring time that is statistically independent of their failure times. The classical approach is considered for estimating the Weibull distribution parameters with non-informative censored samples which occur most often in medical and biological study. We have also considered the Bayesian methods via gamma priors with asymmetric (general entropy) loss function and symmetric (squared error) loss function. A simulation study is carried out to assess the performances of the methods using mean squared errors and absolute biases. Two sets of data have been analysed for the purpose of illustration.

Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors

In this paper, we propose Bayes estimators of the parameter and reliability function of inverted exponential distribution under the general entropy loss function for complete, type I and type II censored samples. The proposed estimators have been compared with the corresponding maximum-likelihood estimators for their simulated risks (average loss over sample space).

Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction

Robust Bayesian methodology deals with the problem of explaining uncertainty of the inputs (the prior, the model, and the loss function) and provides a breakthrough way to take into account the input’s variation. If the uncertainty is in terms of the prior knowledge, robust Bayesian analysis provides a way to consider the prior knowledge in terms of a class of priors \(\varGamma \) and derive some optimal rules. In this paper, we motivate utilizing robust Bayes methodology under the asymmetric general entropy loss function in insurance and pursue two main goals, namely (i) computing premiums and (ii) predicting a future claim size. To achieve the goals, we choose some classes of priors and deal with (i) Bayes and posterior regret gamma minimax premium computation, (ii) Bayes and posterior regret gamma minimax prediction of a future claim size under the general entropy loss. We also perform a prequential analysis and compare the performance of posterior regret gamma minimax predictors against the Bayes predictors.

Estimation of Parameters of Exponentiated Pareto Distribution for Progressive Type-II Censored Data with Random Removals Scheme

In this paper, we propose maximum likelihood estimators and Bayes estimators of parameters of exponentiated Pareto distribution under general Entropy loss function and squared error loss function for Progressive type-II censored data with binomial removals. The maximum likelihood estimators and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from exponentiated Pareto distribution.

Estimation in Misclassified Size-Biased Generalized Negative Binomial Distribution

In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability ����. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likelihood estimators and Bayes estimators. Also comparison has been made between maximum likelihood estimator and Bayes estimator.

Bayesian inference based on a jointly type-II censored sample from two exponential populations

In this paper, based on a jointly type-II censored sample from two exponential populations, the Bayesian inference for the two unknown parameters are developed with the use of squared-error, linear-exponential and general entropy loss functions. The problem of predicting the future failure times, both point and interval prediction, based on the observed joint type-II censored data, is also addressed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the Bayesian estimators with the maximum likelihood estimator developed by Balakrishnan and Rasouli [Exact likelihood inference for two exponential populations under joint type-II censoring. Comput Stat Data Anal. 2008;52:2725–2738]. Finally, a numerical example is utilized for the purpose of illustration.

Estimation for the Type-II Extreme Value Distribution Based on Progressive Type-II Censoring

In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes estimates using both the symmetric and asymmetric loss functions via squared error loss, LINEX loss, and general entropy loss functions. Bayes estimates are obtained using the idea of Lindley and Markov chain Monte Carlo techniques. Finally, Monte Carlo simulations are presented to illustrate the methods discussed in this paper. Analysis is also carried out for a real data set.

Bayesian Estimation For The Burr Type III Distribution Under Type II Doubly Censored Data

In this paper, we consider the problem of estimating the parameters and reliability function of the burr Type IIIdistribution based on Type II Doubly censored sample. We use the Bayesian procedures to obtain the estimators ofparameter and reliability function of burr Type III distribution under symmetric (squared-error) and asymmetric(Linex and general entropy)loss functions.

Bayesian Estimation for Deformed Modified Power Series Distribution

In this article, posterior distribution, posterior moments, and predictive distribution for the modified power series distributions deformed at any of a support point under linex and generalized entropy loss function are derived. It is assumed that the prior information can be summarized by a uniform, Beta, two-sided power, Gamma, or generalized Pareto distributions. The obtained results are demonstrated on the generalized Poisson and the generalized negative binomial distribution deformed at a given point.

Evaluating the Lifetime Performance Index Based on the Bayesian Estimation for the Rayleigh Lifetime Products with the Upper Record Values

Quality management is very important for many manufacturing industries. Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. Hence, the lifetime performance indexCLis utilized to measure the performance of product, whereLis the lower specification limit. This study constructs a Bayesian estimator ofCLunder a Rayleigh distribution with the upper record values. The Bayesian estimations are based on squared-error loss function, linear exponential loss function, and general entropy loss function, respectively. Further, the Bayesian estimators ofCLare utilized to construct the testing procedure forCLbased on a credible interval in the condition of knownL. The proposed testing procedure not only can handle nonnormal lifetime data, but also can handle the upper record values. Moreover, the managers can employ the testing procedure to determine whether the lifetime performance of the Rayleigh products adheres to the required level. The hypothesis testing procedure is a quality performance assessment system in enterprise resource planning (ERP).

Bayesian Estimation of the Parameter of Rayleigh Distribution under the Extended Jeffrey’s Prior

In this paper, Bayes estimators of Rayleigh parameter and its associated risk based on extended Jeffrey's prior under the assumptions of both symmetric loss function (squared error loss) and asymmetric (precautionary and general entropy ) loss function have been derived. We also derive the highest posterior density (HPD) and equal-tail prediction intervals for the parameter as well as the HPD prediction intervals for future observation. Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different situations. Finally, An illustrative example is presented to assess how the Rayleigh distribution fits a real data set.

Bayesian Estimation in the Proportional Hazards Model of Random Censorship under Asymmetric Loss Functions

In this paper, we consider the Bayesian estimation of parameters in the proportional hazards model of random censorship for the Weibull distribution under different asymmetric loss functions. It is well-known for the Weibull distribution that a joint conjugate prior on the parameters does not exist; we use both the informative and noninformative priors on the model parameters. Bayes estimates under LINEX and general entropy loss functions are obtained using the Gibbs sampling scheme. A simulation study is carried out to observe the behavior of the proposed estimators for different sample sizes and for different censoring parameters. It is observed that the Bayes estimators under LINEX and general entropy loss functions can be used effectively with the appropriate choice of respective loss function parameters. One real data set is analyzed for illustrative purposes.

Empirical Bayes Estimators of Parameter and Reliability Function for Compound Rayleigh Distribution under Record Data.

Based on the record samples, the empirical Bayes estimators of parameter and reliability function for Compound Rayleigh distribution is investigated under the symmetric and asymmetric loss function. In this case the symmetric loss function is squared error and for the asymmetric loss functions, we consider LINEX and general Entropy loss function.

Bayesian Analysis of the Survival Function and Failure Rate of Weibull Distribution with Censored Data

The survival function of the Weibull distribution determines the probability that a unit or an individual will survive beyond a certain specified time while the failure rate is the rate at which a randomly selected individual known to be alive at time (t − 1) will die at time (t). The classical approach for estimating the survival function and the failure rate is the maximum likelihood method. In this study, we strive to determine the best method, by comparing the classical maximum likelihood against the Bayesian estimators using an informative prior and a proposed data‐dependent prior known as generalised noninformative prior. The Bayesian estimation is considered under three loss functions. Due to the complexity in dealing with the integrals using the Bayesian estimator, Lindley’s approximation procedure is employed to reduce the ratio of the integrals. For the purpose of comparison, the mean squared error (MSE) and the absolute bias are obtained. This study is conducted via simulation by utilising different sample sizes. We observed from the study that the generalised prior we assumed performed better than the others under linear exponential loss function with respect to MSE and under general entropy loss function with respect to absolute bias.

ESTIMATION OF PARAMETERS AND RELIABILITY FUNCTION OF EXPONENTIATED EXPONENTIAL DISTRIBUTION: BAYESIAN APPROACH UNDER GENERAL ENTROPY LOSS FUNCTION

In this Paper we propose Bayes estimators of the parameters of Exponentiated Exponential distribution and Reliability functions under General Entropy loss function for Type II censored sample. The proposed estimators have been compared with the corresponding Bayes estimators obtained under Squared Error loss function and maximum likelihood estimators for their simulated risks (average loss over sample space).