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A uniform approximation to the sampling distribution of the coefficient of variation

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  • Hürlimann, Werner

Abstract

According to Hendricks and Robey (1936) the coefficient of variation from a normal population with sample size n can be approximated by a function defined on the positive real line, which depends on the standard normal moment of order n - 1 about some well-defined point. Simple conditions under which this approximation is valid are derived. It is shown that the approximation error depends upon a standard normal stop-loss moment of order n - 1 about some point. As a main result we obtain a uniform error bound to the exact sampling density of the order of magnitude exp (- n/2k2), where k is the coefficient of variation.

Suggested Citation

  • Hürlimann, Werner, 1995. "A uniform approximation to the sampling distribution of the coefficient of variation," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 263-268, August.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:3:p:263-268
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    References listed on IDEAS

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    1. Gerber, Hans U., 1984. "Error bounds for the compound poisson approximation," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 191-194, July.
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