Journal of Data Science and Modeling

The Beta Modified Exponential Power Series Distribution: Properties and Applications

Document Type : Research Manuscript

Authors

Arezoo Asoodeh 1
Amir Hossein Ghatari 2
Ehsan Bahrami Samani 1

1 Department of Statistics, Faculty of Mathematical Science, Shahid Beheshti University, Tehran, Iran.

2 Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.

https://doi.org/10.22054/jdsm.2024.77694.1040
Abstract
We propose a novel parametric distribution, termed the Beta Modified Exponential Power Series (BMEPS) distribution, capable of modeling increasing, decreasing, bathtub-shaped, and unimodal failure rates. Constructed from addressing a latent complementary risk problem, this distribution arises from a combination of the Beta Modified Exponential (BME) and power series distributions. Within this new distribution, several important distributions discussed in the literature, such as the Beta Modified Exponential Poisson (BMEP), Beta Modified Exponential Geometric (BMEG), and Beta Modified Exponential Logarithmic (BMEL) distributions, exist as special submodels. This work provides a comprehensive mathematical treatment of the new distribution, offering closed-form expressions for its density, cumulative distribution, survival function, failure rate function, the r-th raw moment, and moments of order statistics. Furthermore, we delve into maximum likelihood estimation and present formulas for the elements comprising the Fisher information matrix. Finally, to showcase the flexibility and potential applicability of the new distribution, we apply it to a real dataset.

Keywords

Beta modified exponential distribution
Power series distributions
Goodness-of-fit Tests
Hazard Function
Residual life function
Subjects
Journal of Data Science and Modeling
Volume 2, Issue 1 - Serial Number 3
December 2023
Pages 95-114

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