A Generalization of the V/V_max Test

摘要

The formal V/V_max test is generalized to any kind of object distribution. This task is realized by intro- ducing a new statistic, n_max which takes into account the luminosity function of the objects. Our analysis shows that the values of n_max are uniformly distributed in the interval [0, 1] and the expecta- tion value of (n_max) is 1/2 in any kind of distribution of the objects if the luminosity function adopted is correct. Besides the (n_max) test, we suggest another analysis which could test the uniformity of the distribution of the values of n_max. These two kinds of test provide a strict constraint on the selection of luminosity functions.