A Flexible Extension of the Power Function Distribution: Properties and Applications

Uchenna Uwadi; Uchechukwu George; Elebe  Nwezza; Victor Ogbuehi

doi:10.66721/8nysxn20

Authors

Uchenna Uwadi Alex Ekwueme Federal University Ndufu Alike Ikwo Author
Dr. Uchechukwu George Michael Okpara University of Agriculture, Umudike, Nigeria Author
Dr. Elebe E. Nwezza Alex Ekwueme Federal University Ndufu-Alike Author
Dr. Victor C. Ogbuehi Michael Okpara University of Agriculture, Umudike, Nigeria Author

DOI:

https://doi.org/10.66721/8nysxn20

Keywords:

Power Function Distribution, Exponentiated Gumbel-G, Reliability, Estimation, Simulation

Abstract

This paper introduces a new extension of the Power Function Distribution, referred to as the Exponentiated Gumbel Power Function (EGuPF) distribution derived from the exponentiated Gumbel family of distributions using the power function as the baseline distribution. The EGuPF distribution extends the classical power function distribution by incorporating additional shape parameters, thereby enabling it to capture J-shaped, reverse J-shaped, and bathtub-shaped hazard rate behaviours. The new distribution is expressed as an infinite linear combination of a power function distribution. The quantile function, moments, incomplete moments, Trimmed-L Moments, mode, Moment of Residual Life (MRL), Moment of Reversed Residual Life (MRRL), entropy, and order statistics of EGuPF distribution are derived. Parameter estimation is carried out using the maximum likelihood estimation (MLE) method, and the performance of the estimators is evaluated through Monte Carlo simulation. Simulation results show that the estimators of the parameters of the EGuPF distribution are consistent, efficient, and reliable. The application of the EGuPF distribution is demonstrated using two real datasets: survival times of acute myelogenous leukaemia patients and monthly tax revenue data. In both cases, EGuPF distribution outperforms competing distributions with the same baseline, achieving the lowest AIC, BIC, and goodness-of-fit statistics. These findings establish the EGuPF distribution as a flexible and robust model for analyzing bounded and skewed data.

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