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

In both Tweedie and geometric Tweedie models, the common power parameter $p\mathrm{\notin }(0,1)$ works as an automatic distribution selection. It mainly separates two subclasses of semicontinuous ($1<p<2$) and positive continuous ($p\ge 2$) 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 ($1<p\le 2$) 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.