Estimation of the shape parameter in the inverse Pareto model: a deep dive into loss function performance

This study investigates the comparative efficacy of three non-informative priors and eight loss functions for estimating the shape parameter of the Inverse Pareto distribution, assuming known scale parameter values. The study aims to identify an optimal prior in the absence of prior information and determine the most suitable loss function for precise estimation of the shape parameter. A comprehensive simulation study based on income data evaluates the performance of these priors and loss functions using key statistical metrics, including posterior variances, skewness coefficients, excess kurtosis, and Bayes risks, to derive scientifically robust conclusions.