I have a dataset to analysis and the following information is known: $y_i \sim N(\mu_i, \theta(\mu_i)^2)$ The link function is => $ln(\mu_i) = (\beta)^T X$
$y_i$s are count data. The model parameter is beta and theta. I need to find an estimation method and fit a model.
I have looked at the over-dispersion model and negative binomial models. But they don't seem quite right ... Can anybody point me to the right direction ...? :)
Update: After some more research - I am looking for if there is any R-package will model data with the above properties?