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X-exponential-G Family of Distributions With Applications

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  • Shahid Mohammad

Abstract

A new family of continuous distributions called the X-exponential-G (XE-G) family is proposed. Explicit expressions are derived for the ordinary and incomplete moments, generating functions, mean deviation about the mean and median, Shannon and R\'{e}nyi entropies, and order statistics of this new family. Estimation of the parameters of the new family is done using the method of maximum likelihood. Assessment of the performance of the maximum likelihood estimates is carried out through a simulation study using the quantile function of the XE-G distribution. The usefulness of this new family is illustrated by modeling two real datasets.

Suggested Citation

  • Shahid Mohammad, 2025. "X-exponential-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 13(1), pages 1-40, January.
    • Handle: RePEc:ibn:ijspjl:v:13:y:2025:i:1:p:40
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    References listed on IDEAS

    as
    1. Hadeel Klakattawi & Dawlah Alsulami & Mervat Abd Elaal & Sanku Dey & Lamya Baharith, 2022. "A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-29, February.
    2. M. S. Eliwa & M. El-Morshedy, 2019. "Bivariate Gumbel-G Family of Distributions: Statistical Properties, Bayesian and Non-Bayesian Estimation with Application," Annals of Data Science, Springer, vol. 6(1), pages 39-60, March.
    3. 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.
    4. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    5. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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