scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

scholarly journals Bound lengths for type-I progressive hybrid burr type-XII censored data under SS-PALT

2021 ◽  
Vol 10 (1) ◽  
pp. 4-22
Author(s):  
Gyan Prakash
Keyword(s):  
Confidence Intervals ◽  
Asymptotic Variance ◽  
Real Data ◽  
Accelerated Life Test ◽  
Type I ◽  
Unknown Parameters ◽  
Data Set ◽  
Ml Estimation ◽  
Hybrid Censoring ◽  
Burr Type Xii

Our main focus on combining two different approaches, Step-Stress Partially Accelerated Life Test and Type-I Progressive Hybrid censoring criteria in the present article. The fruitfulness of this combination has been investigated by bound lengths for unknown parameters of the Burr Type-XII distribution. Approximate confidence intervals, Bootstrap confidence intervals and One-Sample Bayes prediction bound lengths have been obtained under the above scenario. Particular cases of Type-I Progressive Hybrid censoring (Type-I and Progressive Type-II censoring) has also evaluated under SS-PALT. Optimal stress change time also measured by minimizing the asymptotic variance of ML Estimation. A simulation study based on Metropolis-Hastings algorithm have carried out along with a real data set example.

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

scholarly journals The lifetime analysis of the Weibull model based on Generalized Type-I progressive hybrid censoring schemes

2022 ◽  
Vol 19 (3) ◽  
pp. 2330-2354
Author(s):  
M. Nagy ◽  
◽  
Adel Fahad Alrasheedi
Keyword(s):  
Real Data ◽  
Weibull Model ◽  
Data Sets ◽  
Type I ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Hybrid Censoring ◽  
Lifetime Analysis ◽  
Failure Point ◽  
Generalized Type

<abstract><p>In this study, we estimate the unknown parameters, reliability, and hazard functions using a generalized Type-I progressive hybrid censoring sample from a Weibull distribution. Maximum likelihood (ML) and Bayesian estimates are calculated using a choice of prior distributions and loss functions, including squared error, general entropy, and LINEX. Unobserved failure point and interval Bayesian predictions, as well as a future progressive censored sample, are also developed. Finally, we run some simulation tests for the Bayesian approach and numerical example on real data sets using the MCMC algorithm.</p></abstract>

scholarly journals Estimating the Entropy for Lomax Distribution Based on Generalized Progressively Hybrid Censoring

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1219 ◽  
Author(s):  
Shuhan Liu ◽  
Wenhao Gui
Keyword(s):  
Incomplete Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Lomax Distribution ◽  
Bayesian Estimates ◽  
Squared Error ◽  
General Entropy Loss Function ◽  
Two Parameter

As it is often unavoidable to obtain incomplete data in life testing and survival analysis, research on censoring data is becoming increasingly popular. In this paper, the problem of estimating the entropy of a two-parameter Lomax distribution based on generalized progressively hybrid censoring is considered. The maximum likelihood estimators of the unknown parameters are derived to estimate the entropy. Further, Bayesian estimates are computed under symmetric and asymmetric loss functions, including squared error, linex, and general entropy loss function. As we cannot obtain analytical Bayesian estimates directly, the Lindley method and the Tierney and Kadane method are applied. A simulation study is conducted and a real data set is analyzed for illustrative purposes.

scholarly journals The E-Bayesian Estimation for Lomax Distribution Based on Generalized Type-I Hybrid Censoring Scheme

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kaiwei Liu ◽  
Yuxuan Zhang
Keyword(s):  
Bayesian Estimation ◽  
Credible Interval ◽  
Type I ◽  
Hybrid Censoring ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Linex Loss ◽  
Kolmogorov Smirnov ◽  
Bayesian Estimations ◽  
Generalized Type

This article studies the E-Bayesian estimation of the unknown parameter of Lomax distribution based on generalized Type-I hybrid censoring. Under square error loss and LINEX loss functions, we get the E-Bayesian estimation and compare its effectiveness with Bayesian estimation. To measure the error of E-Bayesian estimation, the expectation of mean square error (E-MSE) is introduced. With Markov chain Monte Carlo technology, E-Bayesian estimations are computed. Metropolis–Hastings algorithm is applied within the process. Similarly, the credible interval for the parameter is calculated. Then, we can compare the MSE and E-MSE to evaluate whose result is more effective. For the purpose of illustration in real datasets, cases of generalized Type-I hybrid censored samples are presented. In order to judge whether the sample data can be directly fitted by the Lomax distribution, we adopt the Kolmogorov–Smirnov tests for evaluation. Finally, we can get the conclusion after comparing the results of E-Bayesian and Bayesian estimation.

scholarly journals Estimating E-Bayesian of Parameters of Inverse Weibull Distribution Using an Unified Hybrid Censoring Scheme

2021 ◽  
pp. 113-122
Author(s):  
Shahram Yaghoobzadeh Shahrastani ◽  
Iman Makhdoom
Keyword(s):  
Monte Carlo Simulation ◽  
Real Data ◽  
Bayesian Estimator ◽  
Type I ◽  
Type Ii ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Inverse Weibull Distribution ◽  
Censoring Scheme

The combination of generalization Type-I hybrid censoring and generalization Type-II hybrid censoring schemes, scheme creates a new censoring called a Unified hybrid censoring scheme. Therefore, in this study, the E-Bayesian estimation of parameters of the inverse Weibull (IW) distribution is obtained under the unified hybrid censoring scheme, and the efficiency of the proposed method was compared with the Bayesian estimator using Monte Carlo simulation and a real data set.

scholarly journals Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-I Hybrid Censoring

2021 ◽  
Vol 9 (5) ◽  
pp. 533-548
Author(s):  
Song Mao ◽  
Bin Liu ◽  
Yimin Shi
Keyword(s):  
Competing Risks ◽  
Bootstrap Method ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Type I ◽  
Unknown Parameters ◽  
Hybrid Censoring ◽  
Simple Step ◽  
Conditional Moment Generating Function ◽  
Generalized Type

Abstract This paper investigates a simple step-stress accelerated lifetime test (SSALT) model for the inferential analysis of exponential competing risks data. A generalized type-I hybrid censoring scheme is employed to improve the efficiency and controllability of the test. Firstly, the MLEs for parameters are established based on the cumulative exposure model (CEM). Then the conditional moment generating function (MGF) for unknown parameters is set up using conditional expectation and multiple integral techniques. Thirdly, confidence intervals (CIs) are constructed by the exact MGF-based method, the approximate normality-based method, and the bias-corrected and accelerated (BCa) percentile bootstrap method. Finally, we present simulation studies and an illustrative example to compare the performances of different methods.

A bivariate Pareto type I models

2017 ◽  
Vol 5 (1) ◽  
pp. 44
Author(s):  
Mervat Abd Elaal ◽  
Hind Alzahrani
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Type I ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Bayesian Estimations

In this paper two new bivariate Pareto Type I distributions are introduced. The first distribution is based on copula, and the second distribution is based on mixture of and copula. Maximum likelihood and Bayesian estimations are used to estimate the parameters of the proposed distribution. A Monte Carlo Simulation study is carried out to study the behavior of the proposed distributions. A real data set is analyzed to illustrate the performance and flexibility of the proposed distributions.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Parametric and Semiparametric Estimations of Bivariate Truncated Type I Generalized Logistic Models driven from Copulas

2017 ◽  
Vol 7 (1) ◽  
pp. 72 ◽  
Author(s):  
Lamya A Baharith
Keyword(s):  
Logistic Models ◽  
Real Data ◽  
Information Criterion ◽  
Logistic Distribution ◽  
Type I ◽  
Copula Functions ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Generalized Logistic Distribution ◽  
Weibull Models

Truncated type I generalized logistic distribution has been used in a variety of applications. In this article, a new bivariate truncated type I generalized logistic (BTTGL) distributional models driven from three different copula functions are introduced. A study of some properties is illustrated. Parametric and semiparametric methods are used to estimate the parameters of the BTTGL models. Maximum likelihood and inference function for margin estimates of the BTTGL parameters are compared with semiparametric estimates using real data set. Further, a comparison between BTTGL, bivariate generalized exponential and bivariate exponentiated Weibull models is conducted using Akaike information criterion and the maximized log-likelihood. Extensive Monte Carlo simulation study is carried out for different values of the parameters and different sample sizes to compare the performance of parametric and semiparametric estimators based on relative mean square error.

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