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The Beta Exponential Power Series Distribution

Author

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  • Nafiseh Khojastehbakht

    (Shahid Beheshti University)

  • Amirhossein Ghatari

    (Amirkabir University of Technolgy)

  • Ehsan Bahrami Samani

    (Shahid Beheshti University)

Abstract

In this paper, we investigate to propose a new statistical distribution based on power series. We introduce a new family of distributions which are constructed based on a latent complementary risk problem and are obtained by compounding Beta Exponential (BE) and Power Series distributions. The new distribution contains, as special sub-models, several important distributions which are discussed in the literature, such as Beta Exponential Poisson (BEP) distribution, Beta Exponential Geometric (BEG) distribution, Beta Exponential Logarithmic (BEL) distribution, Beta Exponential Binomial (BEB) distribution as special cases. The hazard function of the BEPS distributions can be increasing, decreasing or bathtub shaped among others. The comprehensive mathematical properties of the new distribution is provided such as closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the r-th raw moment, maximum likelihood estimation and also the moments of order statistics. The proposed type of distributions is used to modeling simulated and real datasets.

Suggested Citation

  • Nafiseh Khojastehbakht & Amirhossein Ghatari & Ehsan Bahrami Samani, 2023. "The Beta Exponential Power Series Distribution," Annals of Data Science, Springer, vol. 10(5), pages 1157-1178, October.
    • Handle: RePEc:spr:aodasc:v:10:y:2023:i:5:d:10.1007_s40745-022-00414-8
    DOI: 10.1007/s40745-022-00414-8
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    References listed on IDEAS

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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. Saralees Nadarajah & Samuel Kotz, 2004. "The beta Gumbel distribution," Mathematical Problems in Engineering, Hindawi, vol. 2004, pages 1-10, January.
    3. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
    4. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
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