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Discussion of the Danish Data on Large Fire Insurance Losses

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  • Resnick, Sidney I.

Abstract

Alexander McNeil's (1996) study of the Danish data on large fire insurance losses provides an excellent example of the use of extreme value theory in an important application context. We point out how several alternate statistical techniques and plotting devices can buttress McNeil's conclusions and provide flexible tools for other studies.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:27:y:1997:i:01:p:139-151_01
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    1. 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.
    2. Ahmed Z. Afify & Ahmed M. Gemeay & Noor Akma Ibrahim, 2020. "The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data," Mathematics, MDPI, vol. 8(8), pages 1-28, August.
    3. 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.
    4. Sidney Resnick & Gennady Samorodnitsky, 2000. "A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements," Management Science, INFORMS, vol. 46(9), pages 1236-1248, September.
    5. Bernard, Carole & Kazzi, Rodrigue & Vanduffel, Steven, 2020. "Range Value-at-Risk bounds for unimodal distributions under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 9-24.
    6. 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.
    7. Okhli, Kheirolah & Jabbari Nooghabi, Mehdi, 2021. "On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    8. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    9. Fei Wang & Wei Chao, 2018. "A New Perspective on Improving Hospital Energy Administration Based on Recurrence Interval Analysis," Energies, MDPI, vol. 11(5), pages 1-18, May.
    10. Rocco Roberto Cerchiara & Francesco Acri, 2020. "Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data," Risks, MDPI, vol. 8(3), pages 1-19, July.
    11. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    12. Wei Zhao & Saima K Khosa & Zubair Ahmad & Muhammad Aslam & Ahmed Z Afify, 2020. "Type-I heavy tailed family with applications in medicine, engineering and insurance," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
    13. Arthur Charpentier & Emmanuel Flachaire, 2021. "Pareto Models for Risk Management," Dynamic Modeling and Econometrics in Economics and Finance, in: Gilles Dufrénot & Takashi Matsuki (ed.), Recent Econometric Techniques for Macroeconomic and Financial Data, pages 355-387, Springer.
    14. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2024. "Scale Mixture of Gleser Distribution with an Application to Insurance Data," Mathematics, MDPI, vol. 12(9), pages 1-12, May.
    15. Vinicius Ratton Brandi & Beatriz Vaz de Melo Mendes, 2004. "Assessing Drawdown-at-Risk in Brazilian Real Foreign Exchange Rates," Brazilian Review of Finance, Brazilian Society of Finance, vol. 2(2), pages 207-223.
    16. John Sang Jin Kang & Serge B. Provost & Jiandong Ren, 2019. "Moment-Based Density Approximation Techniques as Applied to Heavy-tailed Distributions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(3), pages 1-1, November.
    17. Farias, Rafael B.A. & Montoril, Michel H. & Andrade, José A.A., 2016. "Bayesian inference for extreme quantiles of heavy tailed distributions," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 103-107.
    18. 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.
    19. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.

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