| ON CONFIDENCE INTERVALS FOR THE PRODUCT OF THREE MEANS OF THREE NORMALEY DISTRIBUTED POPULATIONS |
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| 作者姓名： | E.A.YFANTIS Computer Science |
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| 作者单位： | E.A.YFANTIS Computer Science Department，University of Nevada，Las Vegas，NV 89154，U.S.A.G.T.FLATMAN U.S.Environmental Protection Agency，944 E.Harmon，Las Vegas，NV 89193，U.S.A. |
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| 摘 要： | In many environmental applications,such as exposure assessment and risk modelling,the desiredestimate is a random variable computed as the product of three independently distributed randomvariables.These variables may not necessarily have the same mean and variance.The method for findingthe 100(1-α)% confidence interval for the mean of the product random variable has been proposed bysome practitioners as the product of the 100(1-α)% confidence interval of the three means.In this paperwe show that the distribution of the product of three independent normal random variables is not normal.We find the mean and variance of the product distribution.Further,we show that although the meanof the product is equal to the product of the means,the product of the three confidence intervals is nota good approximation of the confidence intervals for the mean of the product variable.The confidenceinterval of the mean of the product variable may be estimated by computer simulation.An algorithmfor estimating the confidence interval for the mean of the product random variable is given.The programimplementing this algorithm is given as an appendix.
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ON CONFIDENCE INTERVALS FOR THE PRODUCT OF THREE MEANS OF THREE NORMALEY DISTRIBUTED POPULATIONS |
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| E.A.YFANTIS Computer Science.ON CONFIDENCE INTERVALS FOR THE PRODUCT OF THREE MEANS OF THREE NORMALEY DISTRIBUTED POPULATIONS[J].Journal of Geographical Sciences,1991(3). |
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| Authors: | EAYFANTIS Computer Science |
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| Abstract: | |
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| Keywords: | Confidence intervals Products of normal random variables Risk/exposure modeling |
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