IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0257762.html
   My bibliography  Save this article

On Bayesian approach to composite Pareto models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0257762
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0257762&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0257762?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2021. "Measuring income inequality: A robust semi-parametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    2. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    3. Muhammad Hilmi Abdul Majid & Kamarulzaman Ibrahim & Nurulkamal Masseran, 2023. "Three-Part Composite Pareto Modelling for Income Distribution in Malaysia," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    4. 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.
    5. 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.
    6. Brewer, Mike & Joyce, Robert & Waters, Tom & Woods, Joseph, 2020. "A method for decomposing the impact of reforms on the long-run income distribution, with an application to universal credit," Economics Letters, Elsevier, vol. 192(C).
    7. 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).
    8. Muhammad Aslam Mohd Safari & Nurulkamal Masseran & Muhammad Hilmi Abdul Majid, 2020. "Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    9. Yuanyuan Zhang & Saralees Nadarajah, 2017. "Flexible Heavy Tailed Distributions for Big Data," Annals of Data Science, Springer, vol. 4(3), pages 421-432, September.
    10. Foellmi, Reto & Martínez, Isabel Z., 2014. "Volatile Top Income Shares in Switzerland? Reassessing the Evolution Between 1981 and 2009," CEPR Discussion Papers 10006, C.E.P.R. Discussion Papers.
    11. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    12. Kevin L. McKinney & John M. Abowd & John Sabelhaus, 2021. "United States Earnings Dynamics: Inequality, Mobility, and Volatility," NBER Chapters, in: Measuring Distribution and Mobility of Income and Wealth, pages 69-104, National Bureau of Economic Research, Inc.
    13. Dadalau Diana, 2012. "Integrated Estimation Model Of The Difficulty Status Of Entreprise," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 4, pages 130-143, December.
    14. Vladimir Hlasny & Paolo Verme, 2022. "The Impact of Top Incomes Biases on the Measurement of Inequality in the United States," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 749-788, August.
    15. Majda Benzidia & Michel Lubrano, 2016. "A Bayesian Look at American Academic Wages: The Case of Michigan State University," AMSE Working Papers 1628, Aix-Marseille School of Economics, France.
    16. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    17. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    18. Omer L. Gebizlioglu & Serap Yörübulut, 2016. "A Pseudo-Pareto Distribution and Concomitants of Its Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1043-1064, December.
    19. D. J. Rasmussen & Scott Kulp & Robert E. Kopp & Michael Oppenheimer & Benjamin H. Strauss, 2022. "Popular extreme sea level metrics can better communicate impacts," Climatic Change, Springer, vol. 170(3), pages 1-17, February.
    20. Nadav Ben Zeev & Tomer Ifergane, 2022. "Firing Restrictions and Economic Resilience: Protect and Survive?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 93-124, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0257762. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.