Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution

Lin, Chien-Tai; Liu, Yu; Li, Yun-Wei; Chen, Zhi-Wei; Okasha, Hassan M.

doi:10.3390/math9243328

Open AccessArticle

Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution

by

Chien-Tai Lin

^1,*

,

Yu Liu

¹,

Yun-Wei Li

¹,

Zhi-Wei Chen

¹ and

Hassan M. Okasha

^2,†

¹

Department of Mathematics, Tamkang University, New Taipei City 251301, Taiwan

²

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

^*

Author to whom correspondence should be addressed.

^†

Current home address: Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt.

Mathematics 2021, 9(24), 3328; https://doi.org/10.3390/math9243328

Submission received: 13 November 2021 / Revised: 13 December 2021 / Accepted: 17 December 2021 / Published: 20 December 2021

(This article belongs to the Section E: Applied Mathematics)

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Abstract

The recent exponentiated generalized linear exponential distribution is a generalization of the generalized linear exponential distribution and the exponentiated generalized linear exponential distribution. In this paper, we study some statistical properties of this distribution such as negative moments, moments of order statistics, mean residual lifetime, and their asymptotic distributions for sample extreme order statistics. Different estimation procedures include the maximum likelihood estimation, the corrected maximum likelihood estimation, the modified maximum likelihood estimation, the maximum product of spacing estimation, and the least squares estimation are compared via a Monte Carlo simulation study in terms of their biases, mean squared errors, and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate its use for modeling a rainfall data from Orlando, Florida.

Keywords: corrected maximum likelihood estimation; least squares estimation; maximum likelihood estimation; maximum product of spacing estimation; Monte Carlo simulation

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MDPI and ACS Style

Lin, C.-T.; Liu, Y.; Li, Y.-W.; Chen, Z.-W.; Okasha, H.M. Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution. Mathematics 2021, 9, 3328. https://doi.org/10.3390/math9243328

AMA Style

Lin C-T, Liu Y, Li Y-W, Chen Z-W, Okasha HM. Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution. Mathematics. 2021; 9(24):3328. https://doi.org/10.3390/math9243328

Chicago/Turabian Style

Lin, Chien-Tai, Yu Liu, Yun-Wei Li, Zhi-Wei Chen, and Hassan M. Okasha. 2021. "Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution" Mathematics 9, no. 24: 3328. https://doi.org/10.3390/math9243328

APA Style

Lin, C.-T., Liu, Y., Li, Y.-W., Chen, Z.-W., & Okasha, H. M. (2021). Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution. Mathematics, 9(24), 3328. https://doi.org/10.3390/math9243328

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Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution

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