The Modified Beta Gompertz Distribution: Theory and Applications

• Main Authors: Ibrahim Elbatal, Farrukh Jamal, Christophe Chesneau, Mohammed Elgarhy, Sharifah Alrajhi
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Mathematics
• Subjects: modified beta generator; gompertz distribution; maximum likelihood estimation
• Online Access: https://www.mdpi.com/2227-7390/7/1/3

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.