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An Investigation of the Use of Weighted Averages in the Estimation of the Mean of a Long-Tailed Claim Size Distribution

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  • Taylor, G. C.

Abstract

The paper discusses the problem of estimating the mean of a long-tailed claim size distribution when the investigator's knowledge of the distribution is only vague. One method of dealing with this problem, the method developed by Johnson and Hey, is examined and found to produce strongly biased estimators. The situation in which a sufficient statistic (but nothing else) for the claim size distribution is known is examined, and an approximately unbiased estimator developed. This estimator is substantially more efficient than the arithmetic mean in some cases. It appears to be quite successful when the sufficient statistic is real-valued. It is of limited use when the sufficient statistic is vector-valued.

Suggested Citation

  • Taylor, G. C., 1978. "An Investigation of the Use of Weighted Averages in the Estimation of the Mean of a Long-Tailed Claim Size Distribution," ASTIN Bulletin, Cambridge University Press, vol. 10(1), pages 87-98, May.
    • Handle: RePEc:cup:astinb:v:10:y:1978:i:01:p:87-98_00
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