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The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μ X and μ Y respectively. First, estimation of μ X /μ Y as a surrogate for E ( X/Y ) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μ X /μ Y is given. Finally, an approximate confidence interval for μ X /μ Y is provided. A grain yield data set is used to illustrate the results. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Lai et al. (2004) studied this question.
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