A New Mixture of Two Components of Exponentiated Family with Applications to Real Life Data Sets
Abd EL-Maksoud, F., AL-Dayian, G., EL-Helbawy, A. (2024). A New Mixture of Two Components of Exponentiated Family with Applications to Real Life Data Sets. EKB Journal Management System, 3(2), 316-340. doi: 10.21608/cjmss.2024.262548.1038
Fatma Gamal Abd EL-Maksoud; Gannat R. AL-Dayian; Abeer A. EL-Helbawy. "A New Mixture of Two Components of Exponentiated Family with Applications to Real Life Data Sets". EKB Journal Management System, 3, 2, 2024, 316-340. doi: 10.21608/cjmss.2024.262548.1038
Abd EL-Maksoud, F., AL-Dayian, G., EL-Helbawy, A. (2024). 'A New Mixture of Two Components of Exponentiated Family with Applications to Real Life Data Sets', EKB Journal Management System, 3(2), pp. 316-340. doi: 10.21608/cjmss.2024.262548.1038
Abd EL-Maksoud, F., AL-Dayian, G., EL-Helbawy, A. A New Mixture of Two Components of Exponentiated Family with Applications to Real Life Data Sets. EKB Journal Management System, 2024; 3(2): 316-340. doi: 10.21608/cjmss.2024.262548.1038

A New Mixture of Two Components of Exponentiated Family with Applications to Real Life Data Sets

Computational Journal of Mathematical and Statistical Sciences
Volume 3, Issue 2, November 2024, Page 316-340  XML PDF (556.86 K)
Document Type: Original Article
DOI: 10.21608/cjmss.2024.262548.1038
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Authors
Fatma Gamal Abd EL-Maksoud1; Gannat R. AL-Dayianorcid 2; Abeer A. EL-Helbawy email orcid 2
1Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt
2Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls' Branch), Cairo, Egypt
Abstract
In this paper, the mixture of two components of exponentiated family is introduced as a new family of continuous distributions. Some general properties of the proposed family are discussed such as the quantile function, moments, moment generating function and order statistics. The maximum likelihood estimation method is used to derive the estimators for the unknown parameters, reliability and hazard rate functions. The mixture of two exponentiated inverted Kumaraswamy distribution is studied as a sub-model from the mixture exponentiated family of distributions. Some statistical properties are studied such as the quantile function, moments, moment generating function and order statistics. Also, the maximum likelihood estimators for the unknown parameters, reliability and hazard rate functions of the mixture exponentiated inverted Kumaraswamy distribution are obtained. A simulation study is conducted to assess the performance of the maximum likelihood estimators of the parameters of the mixture exponentiated inverted Kumaraswamy distribution. Finally, a real data set is applied to ensure the simulated results.
Keywords
Mixture distribution; Exponentiated family; Inverted Kumaraswamy distribution; Identifiability property; maximum likelihood estimation
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