scholarly journals Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew

2020 ◽  
Vol 9 (1) ◽  
pp. 99-122
Author(s):  
Aditi Chaturvedi ◽  
Surinder Kumar
Keyword(s):  
Real Data ◽  
Point Estimation ◽  
Sampling Scheme ◽  
Type Ii ◽  
Data Set ◽  
Testing Procedures ◽  
Type Ii Censoring ◽  
Reliability Characteristics ◽  
Two Measures ◽  
Parametric Functions

In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ , hazard rate h(t) and the two measures of reliability, namely R(t) = P(X > t), where X denotes the lifetime of an item and P = P(X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew . We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average confiddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.

MCMC in Analysis of Progressively First Failure Censored Competing Risks Data for Gompertz Model

2016 ◽  
Vol 13 (10) ◽  
pp. 6662-6670 ◽  
Author(s):  
R. A Bakoban ◽  
G. A Abd-Elmougod
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Life Time ◽  
Real Data ◽  
Asymptotic Distributions ◽  
Type Ii ◽  
Data Set ◽  
Type Ii Censoring ◽  
Gamma Density ◽  
Special Cases

In medical studies or in reliability analysis, it is quite common that the failure of any individual or any item may be attributable to more than one cause. So in this paper, we consider the competing risks model with very general censoring scheme, namely progressive first-failure censored scheme under the Gompertz life time distribution. The results in each of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are a special cases. We provide different methods for the analysis of the model under the assumption of independent causes of failure and Gompertz distribution lifetimes. The maximum likelihood estimators (MLE’s) of the different parameters as well as approximate confidence intervals are presented. Bayesian estimation using MCMC method under the joint prior density as a product of a conditional gamma density and inverted gamma density for unknown Gompertz parameters are presented. The analysis of a real data set to assess the performance of all these estimators, confidence intervals are developed using asymptotic distributions and Bayesian credible intervals for the parameters. The different methods are compared through a simulation study.

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 Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kyeongjun Lee ◽  
Jung-In Seo
Keyword(s):  
Nuisance Parameter ◽  
Estimation Method ◽  
Real Data ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Type Ii Censoring ◽  
Scale Parameters ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.

Choquet Integral with Respect to High Order Extensional L- Measure

2010 ◽  
Vol 44-47 ◽  
pp. 3579-3583 ◽  
Author(s):  
Hsiang Chuan Liu ◽  
Wei Sung Chen ◽  
Chin Chun Chen ◽  
Yu Du Jheng ◽  
Der Bang Wu
Keyword(s):  
Regression Model ◽  
Choquet Integral ◽  
Real Data ◽  
Multiple Regression Model ◽  
High Order ◽  
Data Set ◽  
Model Based ◽  
Result Show ◽  
Two Measures ◽  
Fold Cross Validation

In this paper, a generalized multivalent fuzzy measure of extensional L-measure, called high order extensional L-measure, is proposed. It is proved that if the value of order index is equal to one, this new measure is just the extensional L-measure, and the larger the value of order index is, the more sensitive it is. A real data set with 5- fold cross-validation MSE is conducted, for comparing the performances of the Choquet integral regression model based on this new measure with other four measures, P-measure and λ-measure, and authors’ two measures, L-measure and extensional L-measure, and two traditional regression model, multiple regression model and ridge regression model, the result show that the Choquet integral regression model based on this new measure has the best performance.

scholarly journals Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2080
Author(s):  
E. H. Hafez ◽  
Fathy H. Riad ◽  
Sh. A. M. Mubarak ◽  
M. S. Mohamed
Keyword(s):  
Real Data ◽  
Upper And Lower Bounds ◽  
Type Ii ◽  
Research Project ◽  
Data Set ◽  
Lindley Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests ◽  
Censored Sample

Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

scholarly journals A Software Reliability Model Using Quantile Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Bijamma Thomas ◽  
Midhu Narayanan Nellikkattu ◽  
Sankaran Godan Paduthol
Keyword(s):  
Software Reliability ◽  
Real Data ◽  
Quantile Function ◽  
Data Set ◽  
Reliability Models ◽  
Software Reliability Models ◽  
Software Reliability Model ◽  
Reliability Characteristics ◽  
Proposed Model ◽  
L Moments

We study a class of software reliability models using quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. Inference procedures on parameters of the model based on L-moments are studied. We apply the proposed model to a real data set.

scholarly journals Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 566-571
Author(s):  
Rana A. Bakoban
Keyword(s):  
Exponential Distribution ◽  
Coefficient Of Variation ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Interval Estimate ◽  
Type Ii ◽  
Bayesian Approaches ◽  
Data Set ◽  
Type Ii Censored Data ◽  
Censoring Scheme

AbstractThe coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

scholarly journals Randomized Play-the-Winner Rule in Two-Period Two-Treatment Repeated Measurement Design

2016 ◽  
Vol 38 (3) ◽  
Author(s):  
Uttam Bandyopadhyay ◽  
Atanu Biswas ◽  
Shirsendu Mukherjee
Keyword(s):  
Clinical Trial ◽  
Real Data ◽  
Repeated Measurement ◽  
Sampling Scheme ◽  
Data Set ◽  
Repeated Measurement Design ◽  
Measurement Design ◽  
Set Up

In the clinical trial randomized play-the-winner rule is used with a goal to allocate more patients to the better treatment in course of sampling. Here we provide an application of this sampling scheme in repeated measurement design. We concentrate on the simplest set up, i.e., on two treatments and two periods. We study, both numerically and theoretically, several exact and limiting properties of this design. We consider some related inferential problems. Finally we use a real data set to illustrate the applicability of our proposed design.

A Note on the Prediction of Censored Exponential Lifetimes in a Simple Step-stress Model with Type-II Censoring

2018 ◽  
Vol 70 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Indrani Basak ◽  
N. Balakrishnan
Keyword(s):  
Prediction Interval ◽  
Real Data ◽  
Prediction Methods ◽  
Type Ii ◽  
Survival Times ◽  
Type Ii Censoring ◽  
Conditional Median ◽  
Article Type ◽  
Simple Step ◽  
Squared Prediction Error

In this article, we consider the problem of predicting survival times of units from the exponential distribution which are censored under a simple step-stress testing experiment. In this article, Type-II censoring are considered for the form of censoring. Two kinds of predictors—the maximum likelihood predictors (MLP) and the conditional median predictors (CMPs)—are derived. Some numerical examples are presented to illustrate the prediction methods developed here. Using simulation studies, prediction intervals are generated for these examples. We then compare the MLP and the CMP with respect to mean squared prediction error (MSPE) and the prediction interval. Finally, we used a real data to apply the prediction methods developed in the article.

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