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Fitting Mixtures Of Erlangs To Censored And Truncated Data Using The Em Algorithm

Author

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  • Verbelen, Roel
  • Gong, Lan
  • Antonio, Katrien
  • Badescu, Andrei
  • Lin, Sheldon

Abstract

We discuss how to fit mixtures of Erlangs to censored and truncated data by iteratively using the EM algorithm. Mixtures of Erlangs form a very versatile, yet analytically tractable, class of distributions making them suitable for loss modeling purposes. The effectiveness of the proposed algorithm is demonstrated on simulated data as well as real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:45:y:2015:i:03:p:729-758_00
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    Cited by:

    1. 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.
    2. Alessandro Staino & Emilio Russo & Massimo Costabile & Arturo Leccadito, 2023. "Minimum capital requirement and portfolio allocation for non-life insurance: a semiparametric model with Conditional Value-at-Risk (CVaR) constraint," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    3. 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.
    4. 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.
    5. 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.
    6. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    7. Sebastian Calcetero-Vanegas & Andrei L. Badescu & X. Sheldon Lin, 2023. "Claim Reserving via Inverse Probability Weighting: A Micro-Level Chain-Ladder Method," Papers 2307.10808, arXiv.org, revised Jun 2024.
    8. Fung, Tsz Chai & Badescu, Andrei L. & Lin, X. Sheldon, 2019. "A class of mixture of experts models for general insurance: Theoretical developments," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 111-127.
    9. Mingxing He & Jiahua Chen, 2022. "Strong consistency of the MLE under two-parameter Gamma mixture models with a structural scale parameter," 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. 16(1), pages 125-154, March.
    10. Luis Rincón & David J. Santana, 2022. "Ruin Probability for Finite Erlang Mixture Claims Via Recurrence Sequences," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2213-2236, September.
    11. 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.
    12. 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.
    13. 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.
    14. Bhati, Deepesh & Ravi, Sreenivasan, 2018. "On generalized log-Moyal distribution: A new heavy tailed size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 247-259.
    15. 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.
    16. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    17. Yin, Cuihong & Sheldon Lin, X. & Huang, Rongtan & Yuan, Haili, 2019. "On the consistency of penalized MLEs for Erlang mixtures," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 12-20.
    18. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2016. "Multivariate mixtures of Erlangs for density estimation under censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 429-455, July.

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