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The Modified Beta Gompertz Distribution: Theory and Applications

Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Giza 12613, Egypt
Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63360, Pakistan
Department of Mathematics, LMNO, University of Caen, 14032 Caen, France
Department of Statistics, University of Jeddah, Jeddah 21589, Saudi Arabia
Department of Statistics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Author to whom correspondence should be addressed.
Mathematics 2019, 7(1), 3;
Received: 7 November 2018 / Revised: 11 December 2018 / Accepted: 17 December 2018 / Published: 20 December 2018
(This article belongs to the Special Issue Applied and Computational Statistics)
In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets. View Full-Text
Keywords: modified beta generator; gompertz distribution; maximum likelihood estimation modified beta generator; gompertz distribution; maximum likelihood estimation
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MDPI and ACS Style

Elbatal, I.; Jamal, F.; Chesneau, C.; Elgarhy, M.; Alrajhi, S. The Modified Beta Gompertz Distribution: Theory and Applications. Mathematics 2019, 7, 3.

AMA Style

Elbatal I, Jamal F, Chesneau C, Elgarhy M, Alrajhi S. The Modified Beta Gompertz Distribution: Theory and Applications. Mathematics. 2019; 7(1):3.

Chicago/Turabian Style

Elbatal, Ibrahim, Farrukh Jamal, Christophe Chesneau, Mohammed Elgarhy, and Sharifah Alrajhi. 2019. "The Modified Beta Gompertz Distribution: Theory and Applications" Mathematics 7, no. 1: 3.

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