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In both Tweedie and geometric Tweedie models, the common power parameter$p\notin(0,1)$ works as an automatic distribution selection. It mainlyseparates two subclasses of semicontinuous ($1<p<2$) and positive continuous($p\geq 2$) distributions. Our paper centers around exploring diagnostic toolsbased on the maximum likelihood ratio test and minimum Kolmogorov-Smirnovdistance methods in order to discriminate very close distributions within eachsubclass of these two models according to values of $p$. Grounded on the uniqueequality of variation indices, we also discriminate the gamma and geometricgamma distributions with $p=2$ in Tweedie and geometric Tweedie families,respectively. Probabilities of correct selection for several combinations ofdispersion parameters, means and sample sizes are examined by simulations. Wethus perform a numerical comparison study to assess the discriminationprocedures in these subclasses of two families. Finally, semicontinuous($1<p\leq 2$) distributions in the broad sense are significantly moredistinguishable than the over-varied continuous ($p>2$) ones; and two datasetsfor illustration purposes are investigated.

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