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Loss modeling using Burr mixtures

Author

Listed:
  • S. A. Abu Bakar

    (University of Malaya)

  • Saralees Nadarajah

    (University of Manchester)

  • Z. A. Absl Kamarul Adzhar

    (University of Malaya)

Abstract

The first-ever real data application of a two-component Burr mixture distribution is provided. It is fitted to three loss data sets: fire loss claims in Denmark, fire loss claims for three building categories in Belgium and fire loss data in Norway. Each of these data sets exhibits significant bimodality. The fits of the two-component Burr mixture distribution are compared to those of five other two-component mixture distributions: the two-component Weibull mixture, two-component gamma mixture, two-component Pareto mixture, two-component lognormal mixture and the two-component exponential mixture distributions. The Burr mixture distribution is shown to give the best fit for each data set. The relative performances of the fitted distributions were assessed in terms of Akaike information criterion values, Bayesian information criterion values, consistent Akaike information criterion values, corrected Akaike information criterion values, Hannan–Quinn criterion values, density plots and probability–probability plots.

Suggested Citation

  • S. A. Abu Bakar & Saralees Nadarajah & Z. A. Absl Kamarul Adzhar, 2018. "Loss modeling using Burr mixtures," Empirical Economics, Springer, vol. 54(4), pages 1503-1516, June.
    • Handle: RePEc:spr:empeco:v:54:y:2018:i:4:d:10.1007_s00181-017-1269-7
    DOI: 10.1007/s00181-017-1269-7
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    References listed on IDEAS

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    1. Resnick, Sidney I., 1997. "Discussion of the Danish Data on Large Fire Insurance Losses," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 139-151, May.
    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. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    4. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    5. Jaeil Ahn & Bhramar Mukherjee & Stephen B. Gruber & Samiran Sinha, 2011. "Missing Exposure Data in Stereotype Regression Model: Application to Matched Case–Control Study with Disease Subclassification," Biometrics, The International Biometric Society, vol. 67(2), pages 546-558, June.
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    Cited by:

    1. Sarra Ghaddab & Manel Kacem & Christian Peretti & Lotfi Belkacem, 2023. "Extreme severity modeling using a GLM-GPD combination: application to an excess of loss reinsurance treaty," Empirical Economics, Springer, vol. 65(3), pages 1105-1127, September.

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    More about this item

    Keywords

    Loss; Maximum likelihood; Mixture distributions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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