### Journals Information

Mathematics and Statistics Vol. 10(1), pp. 35 - 60
DOI: 10.13189/ms.2022.100104
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## Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation

Noura S. Mohamed *, Moshira A. Ismail , Sanaa A. Ismail
Department of Statistics, Faculty of Economics and Political Science, Cairo University, Giza, Egypt

ABSTRACT

Finite mixture models have been used in many fields of statistical analysis such as pattern recognition, clustering and survival analysis, and have been extensively applied in different scientific areas such as marketing, economics, medicine, genetics and social sciences. Introducing mixtures of new generalized lifetime distributions that exhibit important hazard shapes is a major field of research aiming at fitting and analyzing a wider variety of data sets. The main objective of this article is to present a full mathematical study of the properties of the new finite mixture of the three-parameter Weibull extension model, considered as a generalization of the standard Weibull distribution. The new proposed mixture model exhibits a bathtub-shaped hazard rate among other important shapes in reliability applications. We analytically prove the identifiability of the new mixture and investigate its mathematical properties and hazard rate function. Maximum likelihood estimation of the model parameters is considered. The Kolmogrov-Smirnov test statistic is used to fit two famous data sets from mechanical engineering to the proposed model, the Aarset data and the Meeker and Escobar datasets. Results show that the two-component version of the proposed mixture is a superior fit compared to various lifetime distributions, either one-component or two-component lifetime distributions. The new proposed mixture is a significant statistical tool to study lifetime data sets in numerous fields of study.

KEYWORDS
Weibull Extension Model, Finite Mixture Models, Identifiability, Hazard Rate Function, Mean Residual Life, Skewness, Kurtosis, Maximum Likelihood Estimation, Goodness of Fit Tests

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Noura S. Mohamed , Moshira A. Ismail , Sanaa A. Ismail , "Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation," Mathematics and Statistics, Vol. 10, No. 1, pp. 35 - 60, 2022. DOI: 10.13189/ms.2022.100104.

(b). APA Format:
Noura S. Mohamed , Moshira A. Ismail , Sanaa A. Ismail (2022). Study of the New Finite Mixture of Weibull Extension Model: Identifiability, Properties and Estimation. Mathematics and Statistics, 10(1), 35 - 60. DOI: 10.13189/ms.2022.100104.