Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

EL‐Sagheer, Rashad M.; Almuqrin, Muqrin A.; El-Morshedy, Mahmoud; Eliwa, Mohamed S.; Eissa, Fathy H.; Abdo, Doaa A.

doi:10.3390/sym14050956

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…Especially when data is non-normal, the Bootstrap confidence intervals of different distribution types of non-normal data were studied: such as the Modified Process Capability Index for Wei-bull distribution [19], Parametric and non-parametric bootstrap confidence intervals of CNpk for exponential [20] and exponential power distribution [21], and so on. In addition, its application can also be seen in the case of small samples [22,23]. Bootstrap method replaces theoretical analysis with computer simulation technology, and replaces real distribution with statistical empirical distribution.…”

Section: Related Workmentioning

confidence: 99%

Investigating the Effect of Small Sample Process Capability Index Under Different Bootstrap Methods

Wang,

Bo,

2024

IJACSA

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In the quality control of multi-variety and smallbatch products, the calculation of the process capability index is particularly important. However, when the sample size is not enough, the process distribution cannot be judged, if the traditional method is still used to calculate the process capability index; there will be misapplication or misuse. In this paper, the Bootstrap method is introduced into the estimation of process capability index and the calculation of its confidence interval by using Standard Bootstrap (SB), Percentile Bootstrap (PB), Percentile-t Bootstrap (PTB) and Biased-corrected Percentile Bootstrap (BCPB) methods were used to analyze and compare the process capability index. It is found that in symmetric distribution, only the sample size has a significant effect on the length of the confidence interval；but in asymmetric distribution, sample size and Bootstrap methods are both significant factors affecting the length of confidence interval.

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Section: Related Workmentioning

confidence: 99%

Investigating the Effect of Small Sample Process Capability Index Under Different Bootstrap Methods

Wang,

Bo,

2024

IJACSA

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“…Noninformative priors were used, and samples from the joint posterior distribution were obtained using the random walk Metropolis algorithm. El-Sagheer et al [15] employed Gibbs sampling to estimate the parameters for an asymmetric distribution and various lifetime indices, including reliability and hazard rate functions.…”

Section: = ( ) θ λ α βmentioning

confidence: 99%

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

Srisuradetchai,

Niyomdecha

2024

Symmetry

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This article presents Bayesian estimation methods applied to the gamma zero-truncated Poisson (GZTP) and the complementary gamma zero-truncated Poisson (CGZTP) distributions, encompassing both one-parameter and two-parameter models. These distributions are notably flexible and useful for modeling lifetime data. In the one-parameter model case, the Jeffreys prior is mathematically derived. The use of informative and noninformative priors, combined with the random walk Metropolis algorithm within a Bayesian framework, generates samples from the posterior distributions. Bayesian estimators’ effectiveness is examined through extensive simulation studies, in comparison with the maximum likelihood method. Results indicate that Bayesian estimators provide more precise parameter estimates, even with smaller sample sizes. Furthermore, the study and comparison of the coverage probabilities (CPs) and average lengths (ALs) of the credible intervals with those from Wald intervals suggest that Bayesian credible intervals typically yield shorter ALs and higher CPs, thereby demonstrating the effectiveness of Bayesian inference in the context of GZTP and CGZTP distributions. Lastly, Bayesian inference is applied to real data.

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“…, R m ). Recent years have seen an increase in the amount of literature on PFFC, including in [23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution

Abd-El-Monem,

Eliwa,

El-Morshedy

et al. 2023

Mathematics

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Monitoring life-testing trials for a product or substance often demands significant time and effort. To expedite this process, sometimes units are subjected to more severe conditions in what is known as accelerated life tests. This paper is dedicated to addressing the challenge of estimating the power hazard distribution, both in terms of point and interval estimations, during constant- stress partially accelerated life tests using progressive first failure censored samples. Three techniques are employed for this purpose: maximum likelihood, two parametric bootstraps, and Bayesian methods. These techniques yield point estimates for unknown parameters and the acceleration factor. Additionally, we construct approximate confidence intervals and highest posterior density credible intervals for both the parameters and acceleration factor. The former relies on the asymptotic distribution of maximum likelihood estimators, while the latter employs the Markov chain Monte Carlo technique and focuses on the squared error loss function. To assess the effectiveness of these estimation methods and compare the performance of their respective confidence intervals, a simulation study is conducted. Finally, we validate these inference techniques using real-life engineering data.

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Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

Cited by 5 publications

References 26 publications

Investigating the Effect of Small Sample Process Capability Index Under Different Bootstrap Methods

Investigating the Effect of Small Sample Process Capability Index Under Different Bootstrap Methods

Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data

Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution

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