New alpha power unit distribution: properties and application

Area of Science:

• Probability theory
• Statistical modeling

Background:

• Existing univariate distributions on the unit interval may lack flexibility in hazard function shapes.
• There is a need for new probability models with adaptable characteristics for various applications.

Purpose of the Study:

• To introduce and analyze the two-parameter alpha power unit (APU) probability model.
• To explore the structural properties and practical utility of the APU distribution.
• To demonstrate the flexibility of the APU model compared to existing distributions.

Main Methods:

• Utilizing the parameter-adding method by Mahdavi and Kundu.
• Deriving and discussing key structural properties: quantile function, residual life function, moments, stochastic ordering, and order statistics.
• Employing maximum likelihood estimation (MLE) for parameter estimation, involving non-linear equation solving.

Main Results:

• The APU distribution demonstrates greater flexibility with varied hazard function shapes.
• Structural properties of the APU distribution were derived and analyzed.
• A simulation study confirmed the consistency of the MLE procedure.
• The APU model showed practical applicability through re-analysis of real-life datasets.

Conclusions:

• The proposed alpha power unit (APU) distribution is a flexible and valuable addition to probability models for data on the unit interval.
• The study provides a comprehensive analysis of the APU distribution's properties and demonstrates its practical utility.
• The findings suggest the APU model can effectively analyze real-world data requiring a flexible hazard function.