ISSN:
0886-9383
Keywords:
Confidence intervals
;
Products of normal random variables
;
Risk/exposure modeling
;
Chemistry
;
Analytical Chemistry and Spectroscopy
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
In many environmental applications, such as exposure assessment and risk modelling, the desired estimate is a random variable computed as the product of three independently distributed random variables. These variables may not necessarily have the same mean and variance. The method for finding the 100(1 - α)% confidence interval for the mean of the product random variable has been proposed by some practitioners as the product of the 100(1 - α)% confidence interval of the three means. In this paper we show that the distribution of the product of three independent normal variables is not normal. We find the mean and variance of the product distribution. Further, we show that although the mean of the product is equal to the product of the means, the product of the three confidence intervals is not a good approximation of the confidence intervals for the mean of the product variable. The confidence interval of the mean of the product variable may be estimated by computer simulation. An algorithm for estimating the confidence interval for the mean of the product random variable is given. The program implementing this algorithm is given as an appendix.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cem.1180050317
