Kullback–Leibler life time testing

摘要

The paper deals with testing the hypotheses for homogeneity and point null value of the scale parameter in the gamma family. Tests suggested here are based upon the Kullback–Leibler divergence from an observed vector to the canonical parameter (see Pázman, 1993 [14]), and upon its decomposition. The latter is used to derive the exact distribution of the test statistic by convolution. A geometric integration method is used alternatively to derive the distribution directly. Because it is observed by simulation, that the test’s performance is poor when the shape parameter is estimated from the data, an interval method is developed and its use is demonstrated in an analysis of real data.