Influence measures for the Waring regression model (Q2415501)

The authors of the paper consider a regression model in which the response variable is a count data $y_i\in \{0,1,2\ldots\}$ ($i=1,2,\ldots,n$, $n\in \mathbb{N}$) that follows the Waring$(\mu_i,\phi)$ distribution with parameters having the special form. More exactly, the authors suppose that $y_i$ for all $i=1,2,\ldots,n$ has the following probability function \[ \mathbb{P}(y_i|\mu_i,\phi)=\frac{\phi_1\Gamma(\phi_1+\mu_i\phi_2)\Gamma(y_i+\mu_i\phi_2)}{\Gamma(\mu_i\phi_2) \Gamma(y_i+\phi_1+\mu_i\phi_2+1)}, \ y_i\in\{0,1,2\ldots\}, \] where $\phi_1=2\phi/(\phi-1)$ and $\phi_2=(\phi+1)/(\phi-1)$ with $\mu_i>0$, $\phi>1$. \par A maximum likelihood method to estimate the model parameters is described, diagnostic measures are calculated, an application to real data is presented.