Phenomenological analysis of observed relations for low-redshift galaxies

Maximum-likelihood estimates are made for the exponent p in the phenomenological redshift-distance relation z varies as r/sup p/ for galaxies at redshifts less than or equal to 0.03, on the basis of redshift (z)-magnitude (m)-apparent diameter (theta) observations given in the Reference Catalogue of Bright Galaxies [de Vaucouleurs, G. and de Vaucouleurs, A. (1964)]. The estimates are in the range 1.96 less than or equal to p less than or equal to 2.04 for the full sample of 742 galaxies having m - z - theta data, with dispersions less than or equal to 0.08, and in a similar but broader range for various subsamples. Explicit allowance for an observational cutoff in apparent magnitude in the m - z relation reinforces the result that p is approximately equal 2. Independent estimation based on a cut-off independent generalized Kafka--Schmidt V/V/sub m/ test for a subsample in conservatively limited redshift and magnitude ranges yields p = 2.05