A generalization of the V/V-max test

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