A novel approach for parameter estimation of mixture of two Weibull distributions in failure data modeling

The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixture of Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms of reliability studies and survival analysis. A principal challenge in dealing with MixW lies in the e...

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Published in:	Statistics and computing Vol. 34; no. 6
Main Authors:	Yan, Tianyu, Fang, Kai-Tai, Yin, Hong
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.12.2024 Springer Nature B.V
Subjects:	Algorithms Artificial Intelligence Computer Science Datasets Effectiveness Graphical methods Mixtures Monte Carlo simulation Original Paper Parameter estimation Probability and Statistics in Computer Science Quantiles Reliability analysis Statistical analysis Statistical Theory and Methods Statistics and Computing/Statistics Programs Survival analysis Weibull distribution Parameter estimation Quasi-Monte Carlo SNTO algorithm Weibull probability plot Quantile estimation Mixture of two Weibull distributions
ISSN:	0960-3174, 1573-1375
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Abstract	The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixture of Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms of reliability studies and survival analysis. A principal challenge in dealing with MixW lies in the estimation of parameters. Inspired by the exemplary efficacy of the Quasi-Monte Carlo method in quantile estimation, this paper introduces an innovative approach, which employs the Harrell-Davis and three Sfakianakis and Verginis quantile estimators to enhance the representativeness of the sample, thereby improving the accuracy of parameter estimation. Given the difficulty in deriving analytical expressions for the parameters of MixW and their propensity for convergence to local maxima, this paper adopts the sequential number-theoretic (SNTO) algorithm for the numerical resolution of parameter estimation. The initial optimization region for SNTO is determined via the graphical method of the Weibull probability plot. Simulation studies have demonstrated that our proposed method significantly enhances estimation precision and reduces dependence on the “quality” of the sample. Furthermore, this methodology has been applied to two real data sets that demonstrate the effectiveness of our proposed approach.
AbstractList	The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixture of Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms of reliability studies and survival analysis. A principal challenge in dealing with MixW lies in the estimation of parameters. Inspired by the exemplary efficacy of the Quasi-Monte Carlo method in quantile estimation, this paper introduces an innovative approach, which employs the Harrell-Davis and three Sfakianakis and Verginis quantile estimators to enhance the representativeness of the sample, thereby improving the accuracy of parameter estimation. Given the difficulty in deriving analytical expressions for the parameters of MixW and their propensity for convergence to local maxima, this paper adopts the sequential number-theoretic (SNTO) algorithm for the numerical resolution of parameter estimation. The initial optimization region for SNTO is determined via the graphical method of the Weibull probability plot. Simulation studies have demonstrated that our proposed method significantly enhances estimation precision and reduces dependence on the “quality” of the sample. Furthermore, this methodology has been applied to two real data sets that demonstrate the effectiveness of our proposed approach.
ArticleNumber	221
Author	Yin, Hong Yan, Tianyu Fang, Kai-Tai
Author_xml	– sequence: 1 givenname: Tianyu surname: Yan fullname: Yan, Tianyu organization: School of Mathematics, Renmin University of China – sequence: 2 givenname: Kai-Tai surname: Fang fullname: Fang, Kai-Tai organization: Division of Science and Technology, BNU-HKBU United International College – sequence: 3 givenname: Hong surname: Yin fullname: Yin, Hong email: yinhong@ruc.edu.cn organization: School of Mathematics, Renmin University of China
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Snippet	The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixture of Weibull distributions, serves as an ideal model for...
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SubjectTerms	Algorithms Artificial Intelligence Computer Science Datasets Effectiveness Graphical methods Mixtures Monte Carlo simulation Original Paper Parameter estimation Probability and Statistics in Computer Science Quantiles Reliability analysis Statistical analysis Statistical Theory and Methods Statistics and Computing/Statistics Programs Survival analysis Weibull distribution
Title	A novel approach for parameter estimation of mixture of two Weibull distributions in failure data modeling
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