On Bayesian approach to composite Pareto models

Area of Science:

• Statistics
• Econometrics
• Data Modeling

Background:

• Composite Pareto distribution models are used when data follows different distributions above and below a threshold.
• Existing methods often place prior distributions on the threshold, which can lead to biased estimates.

Purpose of the Study:

• To propose a Bayesian approach for composite Pareto models by specifying prior distributions on the proportion of data from the Pareto distribution.
• To compare the performance of this new approach against traditional methods using simulation studies.

Main Methods:

• Developed a Bayesian framework for composite Pareto models with priors on the proportion parameter.
• Conducted simulation studies to evaluate parameter estimation accuracy.
• Applied the models to real-world income and finance datasets.

Main Results:

• The Bayesian approach with priors on the proportion demonstrated reduced bias in parameter estimates compared to priors on the threshold.
• Simulation results confirmed the improved performance of the proposed method.

Conclusions:

• The proposed Bayesian approach offers a more accurate and less biased method for composite Pareto modeling.
• This technique is particularly useful for analyzing skewed financial and income data.