Empty-boxes test

A statistical test for verifying the hypothesis that an independent sample belongs to a given distribution. More explicitly, let be an independent sample taken from a continuous distribution . The points are chosen so that , . The test is constructed on the basis of the statistic equal to the number of half-intervals in which there is not a single observation . This test has the following form: If , then the hypothesis is accepted; if , then is rejected. The constant is chosen from the condition that the error of the first kind, that is, the probability that is rejected while it is true, is equal to a given value. One may calculate the constant and estimate the power of the empty-boxes test for large and by using limit theorems for random distributions.

References

[1]	V.F. [V.F. Kolchin] Kolčin, B.A. [B.A. Sevast'yanov] Sevast'janov, V.P. [V.P. Chistyakov] Čistyakov, "Random allocations" , Winston (1978) (Translated from Russian)