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Statistical analysis of mixtures underlying probability of ruin
[Štatistická analýza zmesí v pravdepodobnosti ruinovania]

Author

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  • Rastislav Potocký

    (Ústav aplikovanej matematiky a statistiky, Univerzita Komenského, Mlynská Dolina, 842 48 Bratislava, Slovenská republika)

  • Milan Stehlík

    (Ústav aplikované statistiky, JKU Linz, Freistädter Straße 315, A-4040 Linz a. D., Rakousko)

Abstract

If the hypothesis on exponentially distributed claims in a risk (or surplus) model is untenable then, in many cases, the assumption that they are mixtures of two (or more) exponentials is a suitable substitute. In the first part of the paper tests of homogeneity for exponentially distributed claims are discussed and their properties are stated. The statistical properties of parameter estimations for such claims are also mentioned. In the second part the classical Cramer-Lundberg ruin model is discussed when claims are distributed as mixtures of exponentials. Our attention is focussed primarily on assesment of accuracy of approximations obtained. Then our results are compared to those already known.

Suggested Citation

  • Rastislav Potocký & Milan Stehlík, 2009. "Statistical analysis of mixtures underlying probability of ruin [Štatistická analýza zmesí v pravdepodobnosti ruinovania]," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 57(6), pages 209-214.
    • Handle: RePEc:mup:actaun:actaun_2009057060209
    DOI: 10.11118/actaun200957060209
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    References listed on IDEAS

    as
    1. Willmot, Gordon E., 2007. "On the discounted penalty function in the renewal risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 17-31, July.
    2. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Keywords

    ELRH test; ELR2 test; pension pillar; ruin probability;
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