Suppose Y 1 ,...,Y N are independent random variables, each with the Pareto distribution and E(Y i ) = (ß 0 + ß 1 x i ) 2 Is this a generalized linear model? Give reasons for your answer. This is what...

Suppose Y₁,...,Y_N
are independent random variables, each with the Pareto distribution and

E(Y_i) = (ß₀
+ ß₁x_i)²

Is this a generalized linear model? Give reasons for your answer.

This is what I know:

I know that the Pareto distribution is part of the exponential family. So, it meets the first criteria for a generalized linear model.

However, I cannot figure out if this question is canonical, natural, or neither. For example, I know some exponential families are not in the exponential dispersion family used in generalized linear models unless a scale parameter is added and interpreted as a dispersion parameter.

This is what I need help with:

Please explain if this question is canonical, natural, or neither and to recognize the difference.
Thanks!