Half circular modified burr-III distribution, application with different estimation methods.

Area of Science:

• Statistics
• Statistical Modeling
• Circular Data Analysis

Background:

• Axial or half circular data, ranging from 0 to π, are common in medical, environmental, and ecological studies.
• Statistical modeling for half circular data has been underexplored.
• Existing models often lack specialized distributions for this data type.

Purpose of the Study:

• To introduce a novel statistical distribution for half circular data.
• To propose the half circular modified Burr-III (hcMB-III) distribution.
• To evaluate parameter estimation methods for the hcMB-III distribution.

Main Methods:

• The study utilizes inverse stereographic projection on a modified Burr-III distribution to derive the hcMB-III distribution.
• Eight parameter estimation methods are considered: Maximum Likelihood Estimation (MLE) and seven frequentist methods.
• Monte Carlo simulations are employed to assess the performance of these estimation methods.

Main Results:

• The basic properties of the hcMB-III distribution are derived.
• Performance evaluation of the estimation methods was conducted using biases and mean square errors across various sample sizes.
• The proposed hcMB-III model was applied to a real-world dataset of posterior corneal curvature.

Conclusions:

• The hcMB-III distribution offers a new tool for analyzing half circular data.
• The study provides insights into the performance of different parameter estimation techniques for this new distribution.
• The application to corneal curvature data demonstrates the practical utility of the hcMB-III model.