Discriminating between and within (semi)continuous classes of both Tweedie and geometric Tweedie models

Abstract

In both Tweedie and geometric Tweedie models, the common power parameter p (0, 1) works as an automatic distribution selection. It mainly separates two subclasses of semicontinuous (1 < p < 2) and positive continuous (p ≥ 2) distributions. Our paper centers around exploring diagnostic tools based on the maximum likelihood ratio test and minimum Kolmogorov-Smirnov distance methods in order to discriminate very close distributions within each subclass of these two models according to values of p. Grounded on the unique equality of variation indices, we also discriminate the gamma and geometric gamma distributions with p = 2 in Tweedie and geometric Tweedie families, respectively. Probabilities of correct selection for several combinations of dispersion parameters, means and sample sizes are examined by simulations. We thus perform a numerical comparison study to assess the discrimination procedures in these subclasses of two families. Finally, semicontinuous (1 < p ≤ 2) distributions in the broad sense are significantly more distinguishable than the over-varied continuous (p > 2) ones; and two datasets for illustration purposes are investigated.