The Shortest Confidence Interval for the Mean of a Normal Distribution

An interesting topic in mathematical statistics is that of the construction of the confidence intervals. Two kinds of intervals which are both based on the method of pivotal quantity are the shortest confidence interval and the equal tail confidence intervals. The aim of this paper is to clarify and comment on the finding of such intervals and to investigation the relation between the two kinds of intervals. In particular, we will give a construction technique of the shortest confidence intervals for the mean of the standard normal distribution. Examples illustrating the use of this technique are given.

On Shortest Confidence Intervals for Product of Gamma Means

In many environmental applications, such as risk and exposure assessment associated with hazardous waste sites, one is interested in a parameter which can be described as the product of means of several independently distributed gamma variables. In this paper an optimal method of constructing a confidence interval for this parameter is developed. Explicit formulae are given in the case of two independent variables, a situation quite eommon in applications. The proposed prodedure provides a substantial improvement over the commonly used technique of combining individual intervals constructed separately for each mean.