scholarly journals Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

2018 ◽  
Vol 47 (3) ◽  
pp. 40-62 ◽  
Author(s):  
Ankita Chaturvedi ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Real Data ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Type Ii ◽  
Posterior Density ◽  
Numerical Illustration ◽  
Data Set ◽  
Bayesian Procedures ◽  
Credible Intervals ◽  
Highest Posterior Density

This article presents the procedures for the estimation of the parameter of Rayleighdistribution based on Type-II progressive hybrid censored fuzzy lifetime data. Classicalas well as the Bayesian procedures for the estimation of unknown model parameters has been developed. The estimators obtained here are Maximum likelihood (ML) estimator, Method of moments (MM) estimator, Computational approach (CA) estimator and Bayes estimator. Highest posterior density (HPD) credible intervals of the unknown parameter are obtained by using Markov Chain Monte Carlo (MCMC) technique. For numerical illustration, a real data set has been considered.

scholarly journals Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

2021 ◽  
Author(s):  
Hiba Zeyada Muhammed ◽  
Essam Abd Elsalam Muhammed
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Posterior Density ◽  
Data Set ◽  
Bayes Estimates ◽  
Squared Error ◽  
Distribution Shape ◽  
Highest Posterior Density Intervals ◽  
Metropolis Hasting Algorithm ◽  
Highest Posterior Density

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

scholarly journals The Gumbel- Pareto Distribution: Theory and Applications

2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Numerical Illustration ◽  
Data Set ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
First Time ◽  
New Distribution

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

scholarly journals Statistical Inference of the Rayleigh Distribution Based on Progressively Type II Censored Competing Risks Data

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 898 ◽  
Author(s):  
Hongyi Liao ◽  
Wenhao Gui
Keyword(s):  
Competing Risks ◽  
Loss Function ◽  
Information Matrix ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Bayes Estimation ◽  
Type Ii ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Highest Posterior Density

A competing risks model under progressively type II censored data following the Rayleigh distribution is considered. We establish the maximum likelihood estimation for unknown parameters and compute the observed information matrix and the expected Fisher information matrix to construct the asymptotic confidence intervals. Moreover, we obtain the Bayes estimation based on symmetric and non-symmetric loss functions, that is, the squared error loss function and the general entropy loss function, and the highest posterior density intervals are also derived. In addition, a simulation study is presented to assess the performances of different methods discussed in this paper. A real-life data set analysis is provided for illustration purposes.

scholarly journals A Mixture of Two Burr Type III Distributions: Identifiability and Estimation under Type II Censoring

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
A. S. Al-Moisheer
Keyword(s):  
Monte Carlo Simulation ◽  
Real Data ◽  
Reliability Function ◽  
Type Ii ◽  
Estimation Technique ◽  
Numerical Illustration ◽  
Data Set ◽  
Type Ii Censoring ◽  
Type Iii ◽  
Statistical Library

The mixture of two Burr Type III distributions (MTBIIID) is investigated. First, the identifiability property of the MTBIIID is proved. Then, two different methods of estimation are used. Next, the estimates of the unknown five parameters and reliability function of the MTBIIID under Type II censoring are obtained. To study the performance of the estimation technique in the paper, a Monte Carlo simulation is presented. In addition, the numerical illustration requires solving nonlinear equations; therefore, the software international mathematical statistical library (IMSL) is used to assess these effects numerically. Finally, a real data set is applied to illustrate the methods proposed here.

scholarly journals Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Vikas Kumar Sharma
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Model Parameters ◽  
Type Ii ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Highest Posterior Density ◽  
Censoring Scheme

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose.

Revisit to progressively Type-II censored competing risks data from Lomax distributions

2021 ◽  
pp. 1748006X2098397
Author(s):  
Rui Hua ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Linex Loss ◽  
Credible Intervals ◽  
Competing Risks Data ◽  
Highest Posterior Density

In survival analysis, more than one factor typically contributes to individual failure. In addition, censoring is inevitable in lifespan tests or reliability studies due to external causes or experimental purposes. In this article, the competing risks model is considered and investigated under progressively Type-II censoring where data is from Lomax distributions. Assumptions are further made that these competitive factors are independently distributed, and the latent lifetimes of these factors follow Lomax distributions where both scale parameters and shape parameters are different. For all unknown parameters, maximum likelihood estimates have been attained by Newton-Raphson (NR) method as well as expectation maximization (EM) method, and then the approximate confidence intervals are acquired, in addition to bootstrap confidence intervals. Furthermore, under square error and LINEX loss functions, Bayes estimates and corresponding highest posterior density credible intervals are successively constructed. Finally, simulation experiments are implemented to access performance of several proposed methods in this article, and laboratory dataset is presented and analyzed for illustrative purposes.

scholarly journals Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1558
Author(s):  
Ziyu Xiong ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Bootstrap Method ◽  
Information Matrix ◽  
Logistic Distribution ◽  
Type Ii ◽  
Progressive Censoring ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Data Set ◽  
Highest Posterior Density

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

scholarly journals Statistical inferences with jointly type-II censored samples from two Pareto distributions

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 557-565 ◽  
Author(s):  
Hanaa H. Abu-Zinadah
Keyword(s):  
Confidence Intervals ◽  
Life Time ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data ◽  
Data Set ◽  
Censored Samples ◽  
Credible Intervals ◽  
Life Tests ◽  
Censoring Scheme

AbstractIn the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

scholarly journals Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 937 ◽  
Author(s):  
Ying Xie ◽  
Wenhao Gui
Keyword(s):  
Censored Data ◽  
Performance Index ◽  
Manufacturing Industry ◽  
Interval Estimation ◽  
Real Data ◽  
Logistic Distribution ◽  
Posterior Density ◽  
Data Set ◽  
Lifetime Performance ◽  
Highest Posterior Density

Estimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss have a common log-logistic distribution. Both Bayesian and non-Bayesian method are studied. Bayes estimator of the parameters of the log-logistic distribution and the lifetime performance index are obtained using both the Lindley approximation and Monte Carlo Markov Chain methods under symmetric and asymmetric loss functions. As for interval estimation, we apply the maximum likelihood estimator to construct the asymptotic confidence intervals and the Metropolis–Hastings algorithm to establish the highest posterior density credible intervals. Moreover, we analyze a real data set for demonstrative purposes. In addition, different criteria for deciding the optimal censoring scheme have been studied.

scholarly journals Statistical Inference on the Shannon Entropy of Inverse Weibull Distribution under the Progressive First-Failure Censoring

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1209
Author(s):  
Jiao Yu ◽  
Wenhao Gui ◽  
Yuqi Shan
Keyword(s):  
Weibull Distribution ◽  
Importance Sampling ◽  
Complex Form ◽  
Real Data ◽  
Sampling Procedure ◽  
Posterior Density ◽  
Data Set ◽  
Importance Sampling Method ◽  
Inverse Weibull Distribution ◽  
Highest Posterior Density

Entropy is an uncertainty measure of random variables which mathematically represents the prospective quantity of the information. In this paper, we mainly focus on the estimation for the parameters and entropy of an Inverse Weibull distribution under progressive first-failure censoring using classical (Maximum Likelihood) and Bayesian methods. For Bayesian approaches, the Bayesian estimates are obtained based on both asymmetric (General Entropy, Linex) and symmetric (Squared Error) loss functions. Due to the complex form of Bayes estimates, we cannot get an explicit solution. Therefore, the Lindley method as well as Importance Sampling procedure is applied. Furthermore, using Importance Sampling method, the Highest Posterior Density credible intervals of entropy are constructed. As a comparison, the asymptotic intervals of entropy are also gained. Finally, a simulation study is implemented and a real data set analysis is performed to apply the previous methods.

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