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.

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 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 Estimation for Flexible Weibull Extension-Burr XII Distribution under Adaptive Type-II Progressive Censoring Scheme

2021 ◽  
pp. 1065-1094
Author(s):  
Rania M. Kamal ◽  
Moshira A. Ismail
Keyword(s):  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Type Ii ◽  
Progressive Censoring ◽  
Unknown Parameters ◽  
Data Set ◽  
Burr Xii Distribution ◽  
Credible Intervals ◽  
Censoring Scheme

In this paper, based on an adaptive Type-II progressive censoring scheme, estimation of flexible Weibull extension-Burr XII distribution is discussed. Maximum likelihood estimation and asymptotic confidence intervals of the unknown parameters are obtained. The adaptive Metropolis (AM) method is applied to carry out a Bayesian estimation procedure under symmetric and asymmetric loss functions and calculate the credible intervals. A simulation study is carried out to assess the performance of the estimators. Finally, a real life data set is used for illustration purpose.

Improved Confidence Intervals in Quantitative Trait Loci Mapping by Permutation Bootstrapping

Genetics ◽  
2002 ◽  
Vol 160 (4) ◽  
pp. 1673-1686
Author(s):  
Jörn Bennewitz ◽  
Norbert Reinsch ◽  
Ernst Kalm
Keyword(s):  
Quantitative Trait Loci ◽  
Confidence Intervals ◽  
Quantitative Trait ◽  
Bootstrap Method ◽  
Posterior Density ◽  
Nonparametric Bootstrap ◽  
Trait Loci ◽  
Large Width ◽  
The Impact ◽  
Highest Posterior Density

Abstract The nonparametric bootstrap approach is known to be suitable for calculating central confidence intervals for the locations of quantitative trait loci (QTL). However, the distribution of the bootstrap QTL position estimates along the chromosome is peaked at the positions of the markers and is not tailed equally. This results in conservativeness and large width of the confidence intervals. In this study three modified methods are proposed to calculate nonparametric bootstrap confidence intervals for QTL locations, which compute noncentral confidence intervals (uncorrected method I), correct for the impact of the markers (weighted method I), or both (weighted method II). Noncentral confidence intervals were computed with an analog of the highest posterior density method. The correction for the markers is based on the distribution of QTL estimates along the chromosome when the QTL is not linked with any marker, and it can be obtained with a permutation approach. In a simulation study the three methods were compared with the original bootstrap method. The results showed that it is useful, first, to compute noncentral confidence intervals and, second, to correct the bootstrap distribution of the QTL estimates for the impact of the markers. The weighted method II, combining these two properties, produced the shortest and less biased confidence intervals in a large number of simulated configurations.

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 Estimation of Unknown Parameters of Truncated Normal Distribution under Adaptive Progressive Type II Censoring Scheme

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 49
Author(s):  
Siqi Chen ◽  
Wenhao Gui
Keyword(s):  
Normal Distribution ◽  
Confidence Intervals ◽  
Censored Data ◽  
Likelihood Method ◽  
Type Ii ◽  
Truncated Normal Distribution ◽  
Unknown Parameters ◽  
Progressive Type ◽  
Truncated Normal ◽  
Highest Posterior Density

In reality, estimations for the unknown parameters of truncated distribution with censored data have wide utilization. Truncated normal distribution is more suitable to fit lifetime data compared with normal distribution. This article makes statistical inferences on estimating parameters under truncated normal distribution using adaptive progressive type II censored data. First, the estimates are calculated through exploiting maximum likelihood method. The observed and expected Fisher information matrices are derived to establish the asymptotic confidence intervals. Second, Bayesian estimations under three loss functions are also studied. The point estimates are calculated by Lindley approximation. Importance sampling technique is applied to discuss the Bayes estimates and build the associated highest posterior density credible intervals. Bootstrap confidence intervals are constructed for the purpose of comparison. Monte Carlo simulations and data analysis are employed to present the performances of various methods. Finally, we obtain optimal censoring schemes under different criteria.

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.

Estimation of P(X

2017 ◽  
Vol 34 (7) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
E.V. Gijo
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Quality Characteristic ◽  
Logistic Distribution ◽  
Type Ii ◽  
Finite Sample ◽  
Data Set ◽  
Content Type ◽  
Type Ii Censored Data ◽  
Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

scholarly journals Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

scholarly journals Computation of posterior distribution in Bayesian analysis – application in an intermittently used reliability system

2002 ◽  
Vol 21 (3) ◽  
pp. 78-82
Author(s):  
V. S.S. Yadavalli ◽  
P. J. Mostert ◽  
A. Bekker ◽  
M. Botha
Keyword(s):  
Posterior Distribution ◽  
Jeffreys Prior ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Stationary Rate ◽  
Analysis Application ◽  
Definition Of ◽  
Hpd Intervals ◽  
Highest Posterior Density ◽  
Bayes Procedure

Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.

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