The Modified Beta Gompertz Distribution: Theory and Applications

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 a...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-01, Vol.7 (1), p.3
Main Authors: Elbatal, Ibrahim, Jamal, Farrukh, Chesneau, Christophe, Elgarhy, Mohammed, Alrajhi, Sharifah
Format: Article
Language:English
Subjects:
Flexibility
gompertz distribution
Mathematical models
maximum likelihood estimation
Maximum likelihood estimators
Maximum likelihood method
modified beta generator
Parameter estimation
Parameter modification
Random variables
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7010003