I-divergence based testing with applications to reliability and physics

Abstract

We introduce a test based on the I-divergence from the observed vector to the canonical parameter (see [1]). Such a test is employed for testing for homogeneity and the value of the scale parameter in the exponential family. We illustrate the applicability of such a test for real data on light indicators for aeroplanes. We also show how we can extend such a construction outside the exponential family. This will be shown on the statistical problem to expand the experimental distribution of transverse momenta into Rayleigh distribution in photoemulsion experiments. By such an expansion we will construct a high-efficient testing procedure for testing the hypothesis of the homogeneity.