scholarly journals EM Algorithm for Mixture Distributions Model with Type-I Hybrid Censoring Scheme

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2483
Author(s):  
Tzong-Ru Tsai ◽  
Yuhlong Lio ◽  
Wei-Chen Ting
Keyword(s):  
Expectation Maximization ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Mixture Distributions ◽  
Type I ◽  
Censored Samples ◽  
Censoring Scheme

An expectation–maximization (EM) likelihood estimation procedure is proposed to obtain the maximum likelihood estimates of the parameters in a mixture distributions model based on type-I hybrid censored samples when the mixture proportions are unknown. Three bootstrap methods are applied to construct the confidence intervals of the model parameters. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. Simulation results show that the proposed methods can perform well to obtain reliable point and interval estimation results. Three examples are used to illustrate the applications of the proposed methods.

scholarly journals Balanced Joint Progressively Hybrid Type-I Censoring Samples in Estimating the Lifetime Lomax Distributions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Nada M. Alfaer ◽  
Hassan M. Aljohani
Keyword(s):  
Likelihood Estimation ◽  
Model Parameters ◽  
Type I ◽  
Monte Carlo Simulation Study ◽  
Type I Censoring ◽  
Hybrid Type ◽  
Progressive Type ◽  
Estimation Problems ◽  
Credible Intervals ◽  
Censoring Scheme

The comparative life testing for products from different production lines under joint censoring schemes has received some attention over the past few years. Mondal and Kundu recently used the balanced joint progressive type-II censoring scheme to discuss the comparative exponential and Weibull populations. This paper implements the balanced censoring scheme with a hybrid progressive type-I censoring scheme known as a balanced joint progressive hybrid type-I censoring scheme (BJPHCS). The life Lomax products’ model formulation from two different lines of production with BJPHCS is discussed. The model parameters are estimated under maximum likelihood estimation for point and the corresponding asymptotic confidence intervals. Under independent gamma priors, the Bayes estimators and associated credible intervals are obtained with the help of MCMC technique. The validity of the theoretical results developed in this paper for estimation problems is discussed through numerical example and Monte Carlo simulation study, which report the estimators’ quality. Finally, we give a brief comment describing the numerical results.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals A Progressive Interval Type-I Censored Life Test Plan for Rayleigh Distribution

2019 ◽  
Vol 48 (3) ◽  
pp. 76-86
Author(s):  
Arun Kaushik
Keyword(s):  
Rayleigh Distribution ◽  
Interval Censoring ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Test Plan ◽  
Type I Censoring ◽  
Progressive Type ◽  
Interval Type ◽  
Censoring Scheme ◽  
Two Parameter

In this paper, we have considered the problem of optimal inspection times for the progressive interval type-I censoring scheme where uncertainty in the process is governed by the two-parameter Rayleigh distribution. Here, we also introduced some optimality criterion and determined the optimum inspection times, accordingly. The effect of the number of inspections and choice of optimally spaced inspection times based on the asymptotic relative efficiencies of the maximum likelihood estimates of the parameters are also investigated. Further, we have discussed the optimal progressive type-I interval censoring plan when the inspection times and the expected proportions of total failures in the experiment are under control.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

scholarly journals HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

scholarly journals Bayesian Estimation and Prediction Based on Progressively First Failure Censored Scheme from a Mixture of Weibull and Lomax Distributions

2020 ◽  
pp. 357-372
Author(s):  
Mohamed M. Mahmoud ◽  
Manal Mohamed Nassar ◽  
Marwa Ahmed Aefa
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Likelihood Estimation ◽  
Bayes Estimation ◽  
Maximum Likelihood Estimates ◽  
Monte Carlo Simulation Study ◽  
Estimation And Prediction ◽  
Censored Samples ◽  
Symmetric Square

This paper develops Bayesian estimation and prediction, for a mixture of Weibull and Lomax distributions, in the context of the new life test plan called progressive first failure censored samples. Maximum likelihood  estimation and Bayes estimation, under informative and non-informative priors, are obtained using Markov Chain Monte Carlo methods, based on the symmetric square error Loss function and the asymmetric linear exponential (LINEX) and general entropy loss functions. The maximum likelihood estimates and the different Bayes estimates are compared via a Monte Carlo simulation study. Finally, Bayesian prediction intervals for future observations are obtained using a numerical example

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