The power of the exponential scores test for an ordinary renewal process against trend alternatives

The power properties of a statistic based on the use of exponential scores which may be used for testing whether a series of events occurring in time form an ordinary renewal process against trend alternatives are examined. Small sample power comparisons under a Lehmann trend alternative are made with an alternative nonparametric test based on a rank trend statistic and with the parametric test when the intervals are exponentially distributed. Finally, some asymptotic efficiency results are developed for limiting trend alternatives.