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On Bayesian approach to composite Pareto models

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  • Muhammad Hilmi Abdul Majid
  • Kamarulzaman Ibrahim

Abstract

In data modelling using the composite Pareto distribution, any observations above a particular threshold value are assumed to follow Pareto type distribution, whereas the rest of the observations are assumed to follow a different distribution. This paper proposes on the use of Bayesian approach to the composite Pareto models involving specification of the prior distribution on the proportion of data coming from the Pareto distribution, instead of assuming the prior distribution on the threshold, as often done in the literature. Based on a simulation study, it is found that the parameter estimates determined when using uniform prior on the proportion is less biased as compared to the point estimates determined when using uniform prior on the threshold. Applications on income data and finance are included for illustrative examples.

Suggested Citation

  • Muhammad Hilmi Abdul Majid & Kamarulzaman Ibrahim, 2021. "On Bayesian approach to composite Pareto models," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-22, September.
    • Handle: RePEc:plo:pone00:0257762
    DOI: 10.1371/journal.pone.0257762
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    References listed on IDEAS

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    1. Corinne Sinner & Yves Dominicy, 2017. "Distributions and Composite Models for Size-Type Data," Chapters, in: Tsukasa Hokimoto (ed.), Advances in Statistical Methodologies and Their Application to Real Problems, IntechOpen.
    2. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & AL-Dhurafi, Nasr Ahmed, 2020. "The power-law distribution for the income of poor households," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    3. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.
    4. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "A robust semi-parametric approach for measuring income inequality in Malaysia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1-13.
    5. Congressional Budget Office, 2019. "The Distribution of Household Income, 2016," Reports 55413, Congressional Budget Office.
    6. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    7. Congressional Budget Office, 2019. "Projected Changes in the Distribution of Household Income, 2016 to 2021," Reports 55941, Congressional Budget Office.
    8. M. S. Aminzadeh & M. Deng, 2019. "Bayesian predictive modeling for Inverse Gamma-Pareto composite distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1938-1954, April.
    9. Dhanushi A. Wijeyakulasuriya & Ephraim M. Hanks & Benjamin A. Shaby & Paul C. Cross, 2019. "Extreme Value-Based Methods for Modeling Elk Yearly Movements," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 73-91, March.
    10. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2019. "A robust and efficient estimator for the tail index of inverse Pareto distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 431-439.
    11. Cabras, Stefano & Castellanos, María Eugenia, 2011. "A Bayesian Approach for Estimating Extreme Quantiles Under a Semiparametric Mixture Model," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 87-106, May.
    12. Barry C. Arnold, 2008. "Pareto and Generalized Pareto Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 7, pages 119-145, Springer.
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    Cited by:

    1. Mathias Silva & Michel Lubrano, 2023. "Bayesian correction for missing rich using a Pareto II tail with unknown threshold: Combining EU-SILC and WID data," AMSE Working Papers 2320, Aix-Marseille School of Economics, France.
    2. Mathias Silva & Michel Lubrano, 2024. "Bayesian inference for income inequality using a Pareto II tail with an uncertain threshold: Combining EU-SILC and WID data," AMSE Working Papers 2429, Aix-Marseille School of Economics, France.
    3. Marco Bee, 2024. "On discriminating between lognormal and Pareto tail: an unsupervised mixture-based approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 251-269, June.

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