Modèle Poissonnien

$\bullet\hspace{2mm} Y_i \sim {\cal P}(\lambda_i) \Rightarrow f_i(y,\beta)=e^{-\lambda_i}\frac{\lambda_i^y}{y!}.$

$\bullet\hspace{2mm} \theta_i=\log (\lambda_i) \Rightarrow b(\theta_i)=e^{\theta_i}$ et $\zeta=1.$

$\bullet\hspace{2mm} Var(Y_i)=\mu_i=\lambda_i.$

$\bullet\hspace{2mm}$fonction variance: Id.

$\begin{array}{lllll} \hspace{-1.8mm}\bullet & \underline{\mbox{Liens:}} & -\mbo... ... & \lambda_i=e^{<t_i,\beta>} & \mbox{lien canonique}=\mbox{Log.}\\ \end{array}$

$\bullet\hspace{2mm} \widehat{r_i}=\frac{y_i-\widehat{y_i}}{\sqrt{\widehat{y_i}}}$ et $\widehat{y_i}=\widehat{\lambda_i}$ et $S.Dev=2\sum_i(y_i\log{\frac{y_i}{\widehat{y_i}}}+\widehat{y_i}-y_i)$.