A COM-Poisson type generalization of the binomial distribution and its properties and applications (vol 87, pg 158, 2014)

It has come to our attention that the results described in Remarks 1 and 2 do not hold, since the joint distribution given by in Eq. (2) (Shmueli et al., 2005) is not marginally compatible, that is, if the Bernoulli variables Z(i) (i = 1,..., m) have a joint distribution given by Eq. (2), then the joint distribution of (Z(1),..., Z(m-1)) is not of the same form, with m replaced by (m - 1), so that Sigma(m)(i=1) Z(i) does not have its distribution in the same form as Sigma(m)(i=1) Z(i) (see Kadane, 2016). The authors thank Dr. Christian Wei ss for alerting us about this point with respect to Remarks 1 and 2. (c) 2014 Elsevier B.V. All rights reserved.