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Moment-Based Density Approximation Techniques as Applied to Heavy-tailed Distributions

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  • John Sang Jin Kang
  • Serge B. Provost
  • Jiandong Ren

Abstract

Several advances are made in connection with the approximation and estimation of heavy-tailed distributions. It is first explained that on initially applying the Esscher transform to heavy-tailed density functions such as the Pareto, Studentt and Cauchy, said densities can be approximated by employing a certain moment-based methodology. Alternatively, density approximants can be obtained by appropriately truncating such distributions or mapping them onto finite supports. These techniques are then extended to the context of density estimation, their validity being demonstrated by means of simulation studies. As well, illustrative actuarial examples are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:3:p:1
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    References listed on IDEAS

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    3. 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.
    4. Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736, December.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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