Threshold effects onV/V max for gamma-ray bursts

The interpretation of the observed-ray burstV/V_max statistic in terms of spatial distributions is model-dependent. Detection of-ray bursts requires the counting rate in one or more detectors to exceed a thresholdC_lim determined from a time-dependent background rateB(t). The sampling depth of the burst detector is thus time-dependent, and, if burst sources are non-uniform in space, the observedV/V_max distribution will be affected byB(t). We demonstrate this effect with a simple geometric distribution of standard candles and argue thatV/V_max statistic without information on threshold variations is insufficient for rigorous data analysis. Peak count rates and threshold values must be given separately for all events in order to facilitate a meaningful comparison of observations with theoretical distribution models.