8.7 The zero-truncated Poisson distribution has probabilities: pr(Y = j) = ej j!(1 e) = j j!(e 1), for j = 1, 2.....

8.7 The zero-truncated Poisson distribution has probabilities:

pr(Y = j) = e−λλj j!(1 − e−λ) = λj j!(eλ − 1), for j = 1, 2.....

Show that Y is a member of the exponential family distribution with canonical parameter log(λ). Discuss how you would fit this model to data when there is a set, (x1, x2,...,xn), of covariates, corresponding to n observations from the zero-truncated Poisson. A botanical application is provided by Ridout and Dem´etrio (1992).