A Bayesian Framework for Estimating Weibull Distribution Parameters: Applications in Finance, Insurance, and Natural Disaster Analysis

Abstract

This research presents a Bayesian framework for parameter estimation in the two-parameter Weibull distribution, with applications in finance and investment data analysis. The Weibull distribution is widely used for modeling stock pricing movements and making uncertain predictions in financial datasets. The proposed Bayesian approach assumes a gamma prior distribution for the scale parameter, with a known shape parameter. A simulation study using simulated financial data compares the Bayesian method with maximum likelihood estimators in terms of accuracy, error accumulation, and computational time across various sample sizes and parameter values. Results indicate the Bayesian approach performs similarly to maximum likelihood for small samples, while demonstrating computational efficiency for larger financial datasets. The proposed Bayesian model's application to simulated financial data showcases its practical relevance in real-world scenarios. This Bayesian framework offers a valuable tool for handling uncertainty and making informed decisions in financial data analysis, providing robust parameter estimation and uncertainty quantification in finance and investment domains.