DISTRIBUTIONS OF PEAK FLUX AND DURATION FOR GAMMA-RAY BURSTS

Many of the important conclusions about gamma-ray bursts follow from t he distributions of various quantities such as peak flux or duration. We show that for astrophysical transients such as bursts, multiple sel ection thresholds can lead to various forms of data truncation, which can strongly affect the distributions obtained from the data if not ac counted for properly. Thus, the data should be considered to form a mu ltivariate distribution. We also Caution that if the variables forming the multivariate distribution are not statistically independent of ea ch other, further biases can result. A general method is described to properly account for these effects, and as a specific example, we extr act the distributions of flux and duration from the BATSE 3B gamma-ray burst data. It is shown that properly accounting for the aforemention ed biases tends to increase the dope of the log N-log S relation at lo w values of S and increases the number of short-duration bursts.