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Studies using the GRB brightness as a distance indicator require a measure ofbrightness with a small intrinsic dispersion (close to a standard candle).There is unfortunately no general agreement on the definition of such aquantity. We show here that the comparison of the size-frequency curvesobtained with various measures of brightness can be used to select the quantitywhich is closer to a standard candle. Our method relies on a few generalassumptions on the burster spatial distribution, namely that nearby burstersare homogeneously distributed in an Euclidean space with no density orluminosity evolution. We apply it to 5 measures of GRB brightness in theCurrent BATSE Catalog and we find that the GRB size-frequency distributiondepends significantly on the energy window used to measure the GRB brightness.The influence of the time window being, in comparison, negligible. Our methodsuggests that the best distance indicator in this Catalog is the fluencemeasured below 100 keV, indicating that GRB luminosities have a smallerintrinsic dispersion below 100 keV than above.Comment: 5 pages (LateX), 2 Postscript figures, Proceedings of the 4th  Huntsville GRB Worksho

Choosing a measure of GRB brightness that approaches a standard candle