INTERPRETATION OF GAMMA-RAY BURST SOURCE COUNT STATISTICS

Ever since the discovery of gamma-ray bursts, the so-called log N-log S relation has been used for determination of their distances and distribution. This task has not been straightforward because of varying thresholds for the detection of bursts. Most of the current analyses of these data are couched in terms of ambiguous distributions, such as the distribution of C(p)/C(lim), the ratio of peak to threshold photon count rates, or the distribution of V/V(max) = (C(p)/C(lim)) - 3/2. It is shown that these distributions are not always a true reflection of the log N-log S relation. Some kind of deconvolution is required for obtaining the true log N-log S. Therefore, care is required in the interpretation of results of such analyses. A new method of analysis of these data is described, whereby the bivariate distribution of C(p) and C(lim) is obtained directly from the data. This is a nonparametric, maximum-likelihood method which docs not require binning of the data. A new method for determination of the stochastic independence of C(p) and C(lim) is also described, and these methods are applied to some of the existing data on gamma-ray bursts.