Different estimation methods of the modified Kies Topp-Leone model with applications and quantile regression

Area of Science:

• Statistics
• Probability Distributions
• Mathematical Modeling

Background:

• Data on the unit interval (0, 1) or [0, 1] requires specialized distributions.
• Existing distributions may not capture the diverse characteristics of such data.
• The Kies Topp-Leone distribution is a known model for interval-bounded data.

Purpose of the Study:

• Introduce the novel modified Kies Topp-Leone (MKTL) distribution.
• Evaluate the performance of various parameter estimation methods for MKTL.
• Demonstrate the MKTL distribution's utility and superiority in real-world data modeling.

Main Methods:

• Development of the modified Kies Topp-Leone (MKTL) distribution.
• Application of twelve distinct parameter estimation techniques.
• Monte Carlo simulation experiments to compare estimation methods.
• Validation using three real-world datasets and comparison with competing models.

Main Results:

• The MKTL distribution exhibits desirable density and hazard rate function shapes.
• Maximum likelihood estimation emerged as the most effective method.
• The MKTL distribution demonstrated superior performance against alternative models.
• The developed quantile regression model based on MKTL provided a competitive fit.

Conclusions:

• The modified Kies Topp-Leone (MKTL) distribution is a flexible and effective tool for modeling unit interval data.
• Maximum likelihood estimation is recommended for MKTL parameter estimation.
• MKTL offers a significant advancement over existing distributions for interval-bounded data analysis.