From my understanding of the question, it seems you would like to model the average, mu, of a response, y, to input variables, X, with a Poisson distribution. For a Poisson regression, the model is transformed with the log link:
log(mu) = beta1 +Z1*beta2 +Z2*beta3
where
beta1 = log(a)
beta2 = log(b)
beta3 = c
Z1 = X1
Z2 = log(X2)
with a, b, c, X1, X2 corresponding to your variables. You can then use "glmfit" (or "fitglm") with 'Distribution' as 'Poisson' and 'Link' as 'Log' with the above transformation to get the desired result. For more information, please see:
