The Modified Beta Gompertz Distribution: Theory and Applications

Ibrahim Elbatal, Farrukh Jamal, Christophe Chesneau, Mohammed Elgarhy and Sharifah Alrajhi
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Ibrahim Elbatal: Institute of Statistical Studies and Research (ISSR), Department of Mathematical Statistics, Cairo University, Giza 12613, Egypt
Farrukh Jamal: Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63360, Pakistan
Christophe Chesneau: Department of Mathematics, LMNO, University of Caen, 14032 Caen, France
Mohammed Elgarhy: Department of Statistics, University of Jeddah, Jeddah 21589, Saudi Arabia
Sharifah Alrajhi: Department of Statistics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2018, vol. 7, issue 1, 1-17

Abstract: 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.

Keywords: modified beta generator; gompertz distribution; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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