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On composite lognormal-Pareto models

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  • David Scollnik

Abstract

Recently, Cooray & Ananda (2005) proposed a composite lognormal-Pareto model for use with loss payments data of the sort arising in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density thereafter. Here we identify and discuss limitations of this composite lognormal-Pareto model which are likely to severely curtail its potential for practical application to real world data sets. In addition, we present two different composite models based on lognormal and Pareto models in order to address these concerns. The performance of all three composite models is discussed and compared in the context of an example based upon a well-known fire insurance data set.

Suggested Citation

  • David Scollnik, 2007. "On composite lognormal-Pareto models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2007(1), pages 20-33.
    • Handle: RePEc:taf:sactxx:v:2007:y:2007:i:1:p:20-33
    DOI: 10.1080/03461230601110447
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    Citations

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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. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    3. Bae, Taehan & Miljkovic, Tatjana, 2024. "Loss modeling with the size-biased lognormal mixture and the entropy regularized EM algorithm," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 182-195.
    4. Johan René van Dorp & Ekundayo Shittu, 2024. "Two-sided distributions with applications in insurance loss modeling," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 827-861, July.
    5. 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.
    6. Li, Zhengxiao & Wang, Fei & Zhao, Zhengtang, 2024. "A new class of composite GBII regression models with varying threshold for modeling heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 45-66.
    7. Girish Aradhye & George Tzougas & Deepesh Bhati, 2024. "A Copula-Based Bivariate Composite Model for Modelling Claim Costs," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    8. 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.
    9. Walena Anesu Marambakuyana & Sandile Charles Shongwe, 2024. "Composite and Mixture Distributions for Heavy-Tailed Data—An Application to Insurance Claims," Mathematics, MDPI, vol. 12(2), pages 1-23, January.

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