Two statistics
![r = [x_{(n)} - x_{(n-1)}]/[x_{(n-1)} - x_{(1)}]](/images/tex/6437.gif)
and

, where

is the

th largest order statistic of a sample of size

, are studied to determine whether a preassigned false-alarm probability can be achieved in signal detection and to determine their probabilities of detection, of which graphs are presented. The underlying distributions are assumed to be of an exponential type.