ON CONFIDENCE INTERVALS FOR THE PRODUCT OF THREE MEANS OF THREE NORMALEY DISTRIBUTED POPULATIONS

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.     

南海北部海域油气资源调查技术及其应用研究——拖缆及海底地震仪联合勘探观测系统研究

拖缆与海底地震仪联合勘探技术在野外地震调查中起着举足轻重的作用,特别是对油气资源的地震调查方法的研究。其中对海底地震仪(OBS)的研究能够给深水油气调查提供有力的保障,OBS在海底的布设是联合采集的关键,对OBS观测系统的研究显得尤为重要,关系到OBS采集的野外资料的总体质量和后期解释。因此,通过研究,可以选择设计最佳的观测系统,为联合勘探技术提供基础数据,降低采集费用、提高作业效率。