scholarly journals Statistical inference on the accelerated competing failure model from the inverse weibull distribution under progressively type-II censored data

2021 ◽  
pp. 97-97
Author(s):  
Ying Wang ◽  
Zai-Zai Yan
Keyword(s):  
Confidence Intervals ◽  
Normal Approximation ◽  
Likelihood Method ◽  
Failure Model ◽  
Unknown Parameters ◽  
Bootstrap Confidence Intervals ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censored Sample ◽  
Better Than

In this paper, the parameter estimation is discussed by using the maximum likelihood method when the available data have the form of progressively censored sample from a constant-stress accelerated competing failure model. Normal approximation and bootstrap confidence intervals for the unknown parameters are obtained and compared numerically. The simulation results show that bootstrap confidence intervals perform better than normal approximation. A thermal stress example is discussed.

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 Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 319 ◽  
Author(s):  
Xuehua Hu ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Type Ii ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Generalized Pareto ◽  
Censored Sample ◽  
Type Ii Censored Sample

In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.

A note on coverage error of bootstrap confidence intervals for quantiles

1993 ◽  
Vol 114 (3) ◽  
pp. 517-531 ◽  
Author(s):  
D. De Angelis ◽  
Peter Hall ◽  
G. A. Young
Keyword(s):  
Confidence Intervals ◽  
Present Note ◽  
Normal Approximation ◽  
Poor Performance ◽  
Density Estimator ◽  
Bootstrap Confidence Intervals ◽  
Coverage Error ◽  
Bootstrap Percentile ◽  
Coverage Accuracy ◽  
Percentile Bootstrap

AbstractAn interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size n−½, where n denotes sample size. By way of contrast, the error would be O(n−1) for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to o(n−½) by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error O(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-t are also analysed.

Reliability Estimation for Hybrid System under Constant-stress Partially Accelerated Life Test with Progressively Hybrid Censoring

2020 ◽  
Vol 14 (1) ◽  
pp. 82-94
Author(s):  
Xiaolin Shi ◽  
Pu Lu ◽  
Yimin Shi
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Reliability Index ◽  
Bootstrap Method ◽  
Accelerated Life Test ◽  
Life Test ◽  
Unknown Parameters ◽  
Bootstrap Confidence Intervals ◽  
Accelerated Life ◽  
Approximate Confidence Intervals

Background: Reliability analysis for the systems with masked data had been studied by many scholars. However, most researches focused on a system that is either series or parallel only, and the component in the system is mainly exponential or Weibull. In engineering practice, it is often seen that the structure of a system is a combination of series and parallel system, and other types of components are also used in the system. So it is important to study the reliability analysis of hybrid systems with modified Weibull components. Objective: For the hybrid system with masked data, the constant stress partial accelerated life test is performed under type-II progressive hybrid censoring. These data from life test are used to estimate unknown parameters and reliability index of system. The research results will not only provide theoretical basis and reference for system reliability assessment but also favor the patents on partial accelerated life test. Methods: Maximum likelihood estimates of unknown parameters are investigated with the numerical method. The approximate confidence intervals, and bootstrap confidence intervals for parameters are constructed by the asymptotic theory and the bootstrap method, respectively. Results: Maximum likelihood estimations of unknown parameters and reliability index of system are derived. The approximate confidence intervals and bootstrap confidence intervals for unknown parameters are proposed. The performance of estimation of unknown parameters and reliability index are evaluated numerically through Monte Carlo method. Conclusion: The performance on maximum likelihood estimation method is effective and satisfying. For the confidence intervals of parameters, bootstrap method outperforms the approximate method.

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.

EMPIRICAL-LIKELIHOOD-BASED CONFIDENCE INTERVALS FOR CONDITIONAL VARIANCE IN HETEROSKEDASTIC REGRESSION MODELS

2010 ◽  
Vol 27 (1) ◽  
pp. 154-177 ◽  
Author(s):  
Ngai Hang Chan ◽  
Liang Peng ◽  
Dabao Zhang
Keyword(s):  
Confidence Intervals ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Variance Reduction ◽  
Normal Approximation ◽  
Conditional Variance ◽  
Likelihood Method ◽  
Simulation Studies ◽  
Likelihood Methods ◽  
Reduction Techniques

Fan and Yao (1998) proposed an efficient method to estimate the conditional variance of heteroskedastic regression models. Chen, Cheng, and Peng (2009) applied variance reduction techniques to the estimator of Fan and Yao (1998) and proposed a new estimator for conditional variance to account for the skewness of financial data. In this paper, we apply empirical likelihood methods to construct confidence intervals for the conditional variance based on the estimator of Fan and Yao (1998) and the reduced variance modification of Chen et al. (2009). Simulation studies and data analysis demonstrate the advantage of the empirical likelihood method over the normal approximation method.

Two-Condition Within-Participant Statistical Mediation Analysis: A Path-Analytic Framework

2019 ◽  
Author(s):  
Amanda Kay Montoya ◽  
Andrew F. Hayes
Keyword(s):  
Confidence Intervals ◽  
Indirect Effect ◽  
Mediation Analysis ◽  
Analytic Approach ◽  
Analytic Framework ◽  
Hypothesis Tests ◽  
Bootstrap Confidence Intervals ◽  
Complex Models ◽  
Path Analytic ◽  
Statistical Mediation Analysis

Researchers interested in testing mediation often use designs where participants are measured on a dependent variable Y and a mediator M in both of two different circumstances. The dominant approach to assessing mediation in such a design, proposed by Judd, Kenny, and McClelland (2001), relies on a series of hypothesis tests about components of the mediation model and is not based on an estimate of or formal inference about the indirect effect. In this paper we recast Judd et al.’s approach in the path-analytic framework that is now commonly used in between-participant mediation analysis. By so doing, it is apparent how to estimate the indirect effect of a within-participant manipulation on some outcome through a mediator as the product of paths of influence. This path analytic approach eliminates the need for discrete hypothesis tests about components of the model to support a claim of mediation, as Judd et al’s method requires, because it relies only on an inference about the product of paths— the indirect effect. We generalize methods of inference for the indirect effect widely used in between-participant designs to this within-participant version of mediation analysis, including bootstrap confidence intervals and Monte Carlo confidence intervals. Using this path analytic approach, we extend the method to models with multiple mediators operating in parallel and serially and discuss the comparison of indirect effects in these more complex models. We offer macros and code for SPSS, SAS, and Mplus that conduct these analyses.

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