Poisson regression model

Suppose that we have a sample of n observations y1, y2, . . . , yn which can be treated as a Poisson distribution, with:

The following variance function:

Furthermore, suppose that we want to let the mean µi (and therefore the variance) depend on a vector of explanatory variables xi. We can adopt a simple linear model of the form:

The linear predictor on the right-hand side of the previous equation can assume any real ...

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