Inference on q-Weibull parameters

Jia, Xiang; Nadarajah, Saralees

doi:10.1007/s00362-017-0951-3

Cited by 7 publications

(16 citation statements)

References 23 publications

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“…But we just report the most commonly used ML and LS estimation method whose results will henceforth be compared with their Bayesian counterparts. Here we will just confine ourselves to report the results already produced by [4].…”

Section: The Frequentist Approach Of Statistical Analysismentioning

confidence: 99%

“…We have used "optim" function of R package to get these estimates. For more details on the estimation of the q-Weibull distribution, please refer to [4].…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…[ 1 3]. The q-type distributions are based on functions that are used in nonextensive statistical mechanics of nonextensive formalism [4].…”

Section: Introductionmentioning

confidence: 99%

“…for > 0 and 0 < q < 2 are shape parameters and > 0 is a scale parameter. Following [4,9] we put = − , and…”

Section: Introductionmentioning

confidence: 99%

“…Due to variety of applications of the q-Weibull distribution, the efficient estimation of the PDF and the CDF of the q-Weibull distribution is the purpose of the present study. Jia et al [4] have recently worked out the classical maximum likelihood (ML) and least-square (LS) estimators for the q-Weibull distribution. We have analyzed the q-Weibull distribution in Bayesian framework to avail the aforesaid advantages the approach.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Examining Complex Systems Using the q-Weibull Distribution in Classical and Bayesian Paradigms

Abbas¹

2020

JSTA

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The q-Weibull distribution is a generalized form of the Weibull distribution and has potential to model complex systems and life time datasets. Bayesian inference is the modern statistical technique that can accommodate uncertainty associated with the model parameters in the form of prior distributions. This study presents Bayesian analysis of the q-Weibull distribution using uninformative and informative priors and the results are compared with those produced by the classical maximum likelihood (ML) and least-squares (LS) estimation methods. A simulation study is also made to compare the competing methods. Different model selection criteria and predicted datasets are considered to compare the inferential methods under study. Posterior analyses include evaluating posterior means, medians, credible intervals of highest density regions, and posterior predictive distributions. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) setup using WinBUGS package. The Bayesian method has proved to be superior to its classical counterparts. A real dataset is used to illustrate the entire inferential procedure.

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Section: The Frequentist Approach Of Statistical Analysismentioning

confidence: 99%

“…We have used "optim" function of R package to get these estimates. For more details on the estimation of the q-Weibull distribution, please refer to [4].…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…[ 1 3]. The q-type distributions are based on functions that are used in nonextensive statistical mechanics of nonextensive formalism [4].…”

Section: Introductionmentioning

confidence: 99%

“…for > 0 and 0 < q < 2 are shape parameters and > 0 is a scale parameter. Following [4,9] we put = − , and…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Examining Complex Systems Using the q-Weibull Distribution in Classical and Bayesian Paradigms

Abbas¹

2020

JSTA

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Reliability analysis of computed tomography equipment using the q‐Weibull distribution

Litian

Zhi

Ling

et al. 2023

Engineering Reports

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Inspired by the successful application of the q‐Weibull distribution in other research fields, we took the lead to use it in the field of medical devices in this work. The parameter estimation of the q‐Weibull distribution was performed using the probability plot method. The CT failure data from Nanfang Hospital in Guangzhou, China, were used to study the reliability of CT equipment at two levels: the CT system and its seven main components. In terms of evaluation accuracy, the mean squared error, Akaike's information criterion, and the determination coefficient were used to compare the accuracy of fitting of different distribution models. The results show that the accuracy of fitting the q‐Weibull distribution is higher than that of the Weibull distribution in terms of determination coefficient and mean squared error. When considering the complexity of the model, the fit accuracy of the Weibull distribution is better. The results were analyzed using reliability and failure rate plots. The q‐Weibull distribution gives a good fit for the failure data of the CT system and components. Though the Weibull distribution fits better in a few cases, the q‐Weibull distribution can describe the entire “bathtub curve” with only a set of parameters. The findings of this study can be extended to other medical devices.

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Reliability analysis for q‐Weibull distribution with multiply Type‐I censored data

Jia

2021

Quality & Reliability Eng

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The widely used Weibull distribution could be generalized to be q-Weibull distribution. To fill out the gap in existing literature, the reliability is studied for q-Weibull distribution with multiply Type-I censored data, which is the general form of Type-I censored data. The point estimates and confidence intervals (CIs) for q-Weibull parameters and reliability parameters such as the reliability and remaining lifetime are all focused on. The maximum likelihood estimates (MLE) are obtained by maximizing the likelihood function and transforming it to an unconstrained optimization problem. The least-square estimates (LSEs) are proposed by minimizing the single-variable profile error function derived from reducing the previous multivariable error function. These improvements could make the computation of point estimates efficient. Concerning the CIs, the asymptotic normality of log-transformed MLE is used to guarantee they fall into the value ranges. Particularly, the closed form for the Fisher information matrix is derived using the missing information principal and is combined with the delta method to construct the CIs for reliability. Besides, the bias-corrected and accelerated (BCa) bootstrap method is also applied. Further, a Monte Carlo simulation study is conducted to compare different point estimates and CIs. Finally, an illustrative example is presented to show the application of the study in this paper.

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Inference on q-Weibull parameters

Cited by 7 publications

References 23 publications

On Examining Complex Systems Using the q-Weibull Distribution in Classical and Bayesian Paradigms

On Examining Complex Systems Using the q-Weibull Distribution in Classical and Bayesian Paradigms

Reliability analysis of computed tomography equipment using the q‐Weibull distribution

Reliability analysis for q‐Weibull distribution with multiply Type‐I censored data

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