A Novel Alpha-Power X Family: A Flexible Framework for Distribution Generation with Focus on the Half-Logistic Model

Area of Science:

• Probability theory
• Statistical modeling
• Distribution theory

Background:

• Classical statistical distributions often lack flexibility for complex data.
• The half-logistic distribution is a useful but limited model.
• Need for adaptable probability distributions in applied sciences.

Purpose of the Study:

• Introduce the novel alpha-power X (NAP-X) family of distributions.
• Develop and analyze the novel alpha-power half-logistic (NAP-HL) distribution.
• Evaluate parameter estimation techniques and demonstrate practical utility.

Main Methods:

• Theoretical derivations of moments, quantile function, and hazard rate for NAP-HL.
• Simulation study comparing seven parameter estimation methods (MLE, CVME, MPSE, LSE, WLSE, ADE, RTADE).
• Application to two real-world datasets from metrology and engineering.

Main Results:

• The NAP-HL distribution offers greater adaptability compared to the classical half-logistic model.
• Comparative analysis of estimation techniques provides insights into their performance.
• NAP-HL model showed a better fit to real datasets than traditional distributions.

Conclusions:

• The proposed NAP-HL distribution is a flexible and valuable addition to statistical modeling.
• The study validates the effectiveness of the NAP-HL model in practical applications.
• Provides guidance on selecting appropriate estimation methods for the new distribution.