In each of the situations, state whether the indicated model can be regarded as a Generalized Linear Model (GLM) and give reasons for your answer. 

Greek letters indicate unknown parameters, $Y_{i}$? denotes the $i^{th}$ observation of a response variable correpsonding to the value $x_{i}$? of an explanatory variable. Assume independent observations for i=1,...,n.

(i) $Y_{i}$? =0 or 1 where P($Y_{i}=1$)= $e^{-\beta x_{i} }$
(ii) $Y_{i} \sim$ exponential with mean $\mu _{i}$ where $\mu _{i} = exp(\beta _{0} + \beta _{1}x _{i})$
(iii) $Y_{i} \sim  $?Poisson with mean $\mu _{i}$? where $\mu _{i} = \eta _{i} e^{(\beta x _{i})}$ and $\eta _{i}$ ? is known.
Commenting to add:

I believe that the answer for (ii) and (iii) are below and need my logic checked, for (i) I don't know how to approach this at all and need help with this.

For the others:

(ii) For exponential the mean given is $\mu _{i} = exp(\beta _{0} + \beta _{1}x _{i})$, thus if we can a log transformation of the mean, this will be a linear combination of XB and thus this is a GLM. Also note that the exponential distribution belongs to the exponential family.

(iii) Similarly, the mean here is $\mu _{i} = \eta _{i} e^{(\beta x _{i})}$, taking log this becomes log($\eta _{i} e^{(\beta x _{i})}$)=log($\eta _{i}) + {(\beta x _{i})}$ which is also a linear form of the predictor variable so this can also be regarded as a Generalized Linear Model. 

Answer

Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer

1 Attachment

The answer is accepted.