MULTIFRACTAL ANALYSIS OF THE GALAXY DISTRIBUTION - RELIABILITY OF RESULTS FROM FINITE DATA SETS

We test the reliability of the different generalized fractal dimension estimators, when applied to point distributions with a priori known s caling properties. We consider the effects of varying the amount of av ailable data and the dimensionality of the distribution. The present w ork is motivated by the growing interest in cosmological context to sa fely analyze the scale-invariant properties of the observed galaxy dis tribution; these results may also be of value in all physical situatio ns where the statistical analysis of a fractal ''dust'' is required. W e consider (a) a monofractal structure with dimension D = 1, (b) a mul tifractal structure, and (c) a scale-dependent structure, behaving lik e a D = 1 monofractal at small scales and an homogeneous dust at large scales. For this structure, the clustering strength and the point num ber density have been chosen as to be similar to those observed for th e galaxy distribution. Although the different methods display differen t advantages and pitfalls, we find that the presently available galaxy samples can be usefully employed to trace the scaling properties gene rated by nonlinear clustering.