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# The Modified Beta Gompertz Distribution: Theory and Applications

by 4 and
1
Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Giza 12613, Egypt
2
Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63360, Pakistan
3
Department of Mathematics, LMNO, University of Caen, 14032 Caen, France
4
Department of Statistics, University of Jeddah, Jeddah 21589, Saudi Arabia
5
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; https://doi.org/10.3390/math7010003
Received: 7 November 2018 / Revised: 11 December 2018 / Accepted: 17 December 2018 / Published: 20 December 2018
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
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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. https://doi.org/10.3390/math7010003

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. https://doi.org/10.3390/math7010003

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. https://doi.org/10.3390/math7010003

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