The Modified Beta Gompertz Distribution: Theory and Applications

Ibrahim M Elbatal (1, 2) , Farrukh Jamal (3) , Christophe Chesneau (4) , Mohammed Elgarhy (5) , Sharifah Alrajhi (6)

1 Department of Mathematics and Statistics
2 IMSIU - Al Imam Mohammad Ibn Saud Islamic University
3 The Islamia University of Bahawalpur - IUB (PAKISTAN)
4 LMNO - Laboratoire de Mathématiques Nicolas Oresme
5 University of Jeddah
6 King Abdulaziz University

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-G 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 phenomenon. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, en-tropies and order statistics. We discuss the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study in order to test validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by means of two applications to real data.

Mots clés: Modified beta generator; Gompertz distribution; Maximum likelihood estimation

Domaines: Statistiques [math.ST]

Ibrahim M Elbatal, Farrukh Jamal, Christophe Chesneau, Mohammed Elgarhy, Sharifah Alrajhi. The Modified Beta Gompertz Distribution: Theory and Applications. 2018. ⟨hal-01912274v2⟩