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.

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

Main Subjects

• Computational Statistics