THE SUPERIORITY OF THE 2-POINT CORRELATION-FUNCTION OVER THE NEAREST-NEIGHBOR ANALYSIS AS A TEST FOR GAMMA-RAY BURST REPETITION

The locations of most gamma-ray bursts are known only to several degre es. As a consequence, to detect repeated outbursts from gamma-ray burs t sources in the largest gamma-ray burst catalogs, one must apply stat istical tests for clustering. I show that the two-point correlation fu nction is superior to the nearest neighbor test for detecting repetiti on whenever the average angle of separation between bursts in the samp le is larger than the location error. The two-point correlation functi on is particularly sensitive to repeating sources that each produce a large number of observed gamma-ray bursts. The effects of Earth blocka ge and the disabling of the burst trigger are examined, and the abilit y of different repetition models to produce an observable repetition s ignal is calculated. I show that only a large number of repetitions pe r source can produce an observable signal, which underscores the stren gth of the two-point correlation function as a test of burst repetitio n. From these results, one must conclude that the deviation from isotr opy found in the BATSE 1B catalog with the nearest neighbor test is a statistical fluctuation, and not a manifestation of burst repetition.