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The gamma-normal distribution: Properties and applications

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  • Alzaatreh, Ayman
  • Famoye, Felix
  • Lee, Carl

Abstract

In this paper, some properties of gamma-X family are discussed and a member of the family, the gamma-normal distribution, is studied in detail. The limiting behaviors, moments, mean deviations, dispersion, and Shannon entropy for the gamma-normal distribution are provided. Bounds for the non-central moments are obtained. The method of maximum likelihood estimation is proposed for estimating the parameters of the gamma-normal distribution. Two real data sets are used to illustrate the applications of the gamma-normal distribution.

Suggested Citation

  • Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:67-80
    DOI: 10.1016/j.csda.2013.07.035
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    References listed on IDEAS

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    6. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
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    Cited by:

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    2. M. Nassar & A. Alzaatreh & O. Abo-Kasem & M. Mead & M. Mansoor, 2018. "A New Family of Generalized Distributions Based on Alpha Power Transformation with Application to Cancer Data," Annals of Data Science, Springer, vol. 5(3), pages 421-436, September.
    3. Zubair Ahmad & M. Elgarhy & G. G. Hamedani, 2018. "A new Weibull-X family of distributions: properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-18, December.
    4. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    5. Ahmad Alzaghal & Duha Hamed, 2019. "New Families of Generalized Lomax Distributions: Properties and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-51, November.
    6. Morad Alizadeh & S. M. T. K. MirMostafee & Edwin M. M. Ortega & Thiago G. Ramires & Gauss M. Cordeiro, 2017. "The odd log-logistic logarithmic generated family of distributions with applications in different areas," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    7. Osama H. Mahmoud Hassan & Ibrahim Elbatal & Abdullah H. Al-Nefaie & Mohammed Elgarhy, 2022. "On the Kavya–Manoharan–Burr X Model: Estimations under Ranked Set Sampling and Applications," JRFM, MDPI, vol. 16(1), pages 1-20, December.

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