Bayesian Analysis of Three-Parameter Frechet Distribution with Medical Applications

Area of Science:

• Statistics
• Biostatistics
• Medical Informatics

Background:

• Medical data in clinical studies often exhibit right-skewed distributions.
• Skewed distributions are suitable for Bayesian inference, aiding decision-making under uncertainty.
• Bayesian estimators can quantify evidence for medical diagnosis, integrating prior information.

Purpose of the Study:

• To develop Bayesian estimators for the three-parameter Frechet distribution.
• To evaluate these estimators under LINEX (linear exponential) and General Entropy (GE) loss functions.
• To compare Bayesian estimates with Maximum Likelihood estimates using simulations.

Main Methods:

• Development of Bayesian estimators for the three-parameter Frechet distribution.
• Application of noninformative and gamma priors.
• Utilizing LINEX and GE loss functions.
• Employing Lindley's approximation for approximate Bayesian estimates.
• Monte Carlo simulations for performance comparison.

Main Results:

• Bayesian estimators under the General Entropy loss function with a noninformative prior (BGENP) demonstrated the smallest mean square error across various sample sizes and parameter values.
• This approach proved superior to Maximum Likelihood estimates.
• The methods were illustrated using patient survival data for head and neck cancer.

Conclusions:

• The BGENP approach offers a robust method for analyzing skewed medical data.
• Bayesian estimation provides a valuable framework for medical decision-making and health management.
• Accurate estimation of skewed distributions is crucial for reliable medical diagnosis and prognosis.