Properties, estimation, and applications of the extended log-logistic distribution

Area of Science:

• Statistics
• Survival Analysis
• Probability Distributions

Background:

• The log-logistic distribution is widely used but has limitations in modeling complex failure rates.
• There is a need for flexible distributions that can capture both monotone and non-monotone hazard rates in survival data.

Purpose of the Study:

• To introduce and analyze the novel exponentiated alpha-power log-logistic (EAPLL) distribution.
• To evaluate the performance of various estimation methods for the EAPLL distribution.
• To demonstrate the EAPLL distribution's utility in modeling real-world survival data.

Main Methods:

• Derivation of key mathematical properties of the EAPLL distribution.
• An extensive simulation study to compare eight different estimation techniques.
• Ranking of estimation methods based on mean estimates, mean square errors, and average absolute biases.
• Application of the EAPLL distribution to three real-life survival datasets.

Main Results:

• The EAPLL distribution provides analytical simplicity and flexibility for survival data.
• The simulation study identified optimal estimation methods for the EAPLL parameters.
• The EAPLL distribution demonstrated superior performance compared to other log-logistic models on real datasets.

Conclusions:

• The exponentiated alpha-power log-logistic (EAPLL) distribution is a valuable addition to survival analysis.
• It offers enhanced capabilities for modeling diverse survival data, including complex failure rate patterns.
• This research provides a robust framework and practical insights for survival data modeling.