Abstract
The I-divergence represents a tool for statistical inference about an unknown parameter gamma of a probability distribution satisfying the following conditions: (i) it belongs to the regular exponential family and (ii) possesses the covering property. We exploit the use of the I-divergence from two different views.
First, we propose a graphical method for I-divergence based testing of parameter gamma exploiting the cumulative distribution function, quantiles of the I-divergence and quantiles of the uniform distribution. The description is followed by the application to simulated exponentially distributed data.
Second, we discuss the decomposition of the I-divergence into two independent elements, both having statistical interpretation in hypothesis testing. The aim of this part is to show the decompositions for several members of the exponential family, namely the exponential, gamma and Pareto distribution.