**3.1 Model performance comparison among variants of** *λ***10***<sup>Y</sup>*

The results of AIC, BIC, and PCS statistical tests are shown in **Table 10** with the goodness ranked in brackets. The following findings are obtained: 1) considering AIC and BIC, the *λ*10*<sup>Y</sup>* model gives better results, since the AIC and BIC values corresponding to the *λ*10*<sup>Y</sup>* model are much smaller than those for the *λ*10*Poi*, *λ*10*NB*, *λ*10*ZIP*, and *λ*10*ZINB* models; 2) in terms of PCS test, the *λ*10*<sup>Y</sup>* model is also the most effective one, since the PCS of *λ*10*<sup>Y</sup>* model is closer to DF (DFs of *λ*10*<sup>Y</sup>*, *λ*10*Poi*, *λ*10*NB*, *λ*10*ZIP*, and *λ*10*ZINB* are considerably approximative).

LL test results are shown in **Table 10**. One can notice that, for the *λ*10*<sup>Y</sup>* model combined with either the Poisson or NB distribution, its GOFs are significantly better than *λ*10*Poi* and *λ*10*NB* models' GOFs according to the LL test. Furthermore, the GOF of *λ*10*<sup>Y</sup>* combined with the NB distribution (NB-*λ*10*<sup>Y</sup>*) is better than when combined with the Poisson distribution (POI-*λ*10*<sup>Y</sup>*).


#### **Table 10.**

*Model GOF comparison among variants of λ*10*<sup>Y</sup>* .
