| For more than two decades, Gamma-Ray Bursts (GRBs) have presented a challenge to astrophysicists. No counterparts in other wavelengths have been found, and their nature and distance from us remain a mystery. They display a wide variety of temporal and spectral characteristics, which has made classification difficult.;This thesis is concerned with the investigation of the spatial distribution of GRBs. The source counts, or the so-called log N-log S relations are the primary data that constrain the spatial distribution of sources such as GRBs whose distances are unknown. In obtaining these relations, however, one must be careful since the GRB data forms a multivariate distribution that contains selection biases. In this work we present and apply a new statistical method that permits us to extract bias-free univariate distributions from the given multivariate distribution. We describe the log N-log S relations not in terms of the commonly used cumulative expression, but in terms of the variation with photon count rate (or photon flux) of its logarithmic slope, a differential quantity which comes out directly from our method. We identify and account for two selection biases in the GRB data: the duration bias caused by the fact that peak photon count rates (or peak photon fluxes) are actually averaged over a triggering time, and the variable threshold bias which introduces a direct truncation in the data.;We check and verify the accuracy of our statistical method through analytical calculations and through Monte Carlo simulations. We then apply it to the following GRB data samples: SMM, SIGNE, GINGA, and BATSE, and discuss how the results deviate from what is expected for a homogeneous, isotropic, stationary, and Euclidean distribution of sources.;The BATSE results are compared with the predictions of cosmological models with a finite range, power-law luminosity function and with pure density and luminosity evolution laws that scale as a power of (1+z). We discuss the limits that may be placed on the range of luminosities and on the evolution. |
