Harris Extended Fréchet Distribution: Properties, Inference, and Applications to Failure and Waiting Time Data

Abstract

We propose and develop the four-parameter Harris Extended Fréchet distribution. It is obtained by inserting the two-parameter Fréchet distribution as the baseline in the Harris family and may be a useful alternative method to model income distribution and could be applied to other areas. We demonstrate that the new distribution can have decreasing, increasing and upside-down-bathtub hazard functions and that its probability density function is an infinite linear combination of Fréchet densities. Some standard mathematical properties of the proposed distribution are derived, such as the quantile function, ordinary and incomplete moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, Renyi and β-entropies, mean residual life and mean inactivity time, probability weighted moments, stress-strength reliability, and order statistics. We also obtain the maximum likelihood estimators of the model. The potentiality/flexibility of the new distribution is illustrated by means two applications to failure and waiting time data sets.

Keywords

Gine index / Bonferroni curve / probability weighted moments / strengthstress reliability

Author Contributions

All authors contributed equally to the production of the manuscript ranging from conceptualization of idea, methodology, software development, original draft preparation, visualization, writing, reviewing and editing. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding; it was funded by the contribution of the authors.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable

Data Availability Statement

The data used for this research are commonly used in the area of research.

Conflicts of Interest

The authors declare no conflict of interests.

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