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On modeling left-truncated loss data using mixtures of distributions

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  • Blostein, Martin
  • Miljkovic, Tatjana

Abstract

A new statistical methodology is developed for fitting left-truncated loss data by using the G-component finite mixture model with any combination of Gamma, Lognormal, and Weibull distributions. The EM algorithm, along with the emEM initialization strategy, is employed for model fitting. We propose a new grid map which considers the model selection criterion (AIC or BIC) and risk measures at the same time, by using the entire space of models under consideration. A simulation study validates our proposed approach. The application of the proposed methodology and use of new grid maps are illustrated through analyzing a real data set that includes left-truncated insurance losses.

Suggested Citation

  • Blostein, Martin & Miljkovic, Tatjana, 2019. "On modeling left-truncated loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 35-46.
    • Handle: RePEc:eee:insuma:v:85:y:2019:i:c:p:35-46
    DOI: 10.1016/j.insmatheco.2018.12.001
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    References listed on IDEAS

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    1. Reynkens, Tom & Verbelen, Roel & Beirlant, Jan & Antonio, Katrien, 2017. "Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 65-77.
    2. Simon Lee & X. Lin, 2010. "Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 107-130.
    3. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    4. Pigeon, Mathieu & Denuit, Michel, 2011. "Composite Lognormal-Pareto model with random threshold," LIDAM Reprints ISBA 2011020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    6. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    7. Stuart Klugman & Jacques Rioux, 2006. "Toward a Unified Approach to Fitting Loss Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(1), pages 63-83.
    8. Verbelen, Roel & Gong, Lan & Antonio, Katrien & Badescu, Andrei & Lin, Sheldon, 2015. "Fitting Mixtures Of Erlangs To Censored And Truncated Data Using The Em Algorithm," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 729-758, September.
    9. Abu Bakar, S.A. & Hamzah, N.A. & Maghsoudi, M. & Nadarajah, S., 2015. "Modeling loss data using composite models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 146-154.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
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    4. Semhar Michael & Tatjana Miljkovic & Volodymyr Melnykov, 2020. "Mixture modeling of data with multiple partial right-censoring levels," 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. 14(2), pages 355-378, June.
    5. Fung, Tsz Chai, 2022. "Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 180-198.
    6. Delong, Łukasz & Lindholm, Mathias & Wüthrich, Mario V., 2021. "Gamma Mixture Density Networks and their application to modelling insurance claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 240-261.
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    8. Počuča, Nikola & Jevtić, Petar & McNicholas, Paul D. & Miljkovic, Tatjana, 2020. "Modeling frequency and severity of claims with the zero-inflated generalized cluster-weighted models," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 79-93.

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    More about this item

    Keywords

    Finite mixture models; EM algorithm; Loss modeling; Left-truncation; Grid map;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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