  An unbinned statistical test on cluster-like deviations from Poisson
processes for point process data is introduced, presented in the context of
time variability analysis of astrophysical sources in count rate experiments.
The measure of deviation of the actually obtained temporal event distribution
from that of a Poisson process is derived from the distribution of time
differences between two consecutive events in a natural way. The differential
character of the measure suggests this test in particular for the search of
irregular burst-like structures in experimental data. The construction allows
the application of the test even for very low event numbers. Furthermore, the
test can easily be applied in the case of varying acceptance of the detector as
well. The simple and direct use of background events simultaneously acquired
under the same conditions to account for acceptance variations is possible,
allowing for easy application especially in earth-bound gamma-ray experiments.
Central features are the fast and simple calculation of its measure, and the
existence of an analytical approximation that describes the general test
statistics to a high degree of precision.
