Abstract
The problem of estimating the unknown upper bound θ on the basis of a sample of sizen from a uniform or rectangular distribution on [0, θ] has considerable interest. This or the analogous discrete version is variously known as the “Taxi-problem” or the “German bomb (or Tank) problem” and has a long history. The emphasis here is on estimation of θ through the lengths of the observed gaps or spacings which seem natural for this problem.
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