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On Bayesian approach to composite Pareto models.

Muhammad Hilmi Abdul Majid1, Kamarulzaman Ibrahim1

  • 1Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia.

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Summary

This study introduces a Bayesian approach for composite Pareto models, focusing on prior distributions for data proportions. This method yields less biased parameter estimates compared to traditional threshold-based priors, improving data modeling accuracy.

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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.