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The Modified Beta Gompertz Distribution: Theory and Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ibrahim Elbatal & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy & Sharifah Alrajhi, 2018. "The Modified Beta Gompertz Distribution: Theory and Applications," Mathematics, MDPI, vol. 7(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:3-:d:192098
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    References listed on IDEAS

    as
    1. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
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