Erratum to “A COM-Poisson type generalization of the binomial distribution and its properties and applications” [Statist. Probab. Lett. 87 (2014) 158–166]

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 ∑ i = 1 m − 1 Z i does not have its distribution in the same form as ∑ i = 1 m Z i (see Kadane, 2016). The authors thank Dr. Christian Weiß for alerting us about this point with respect to Remarks 1 and 2.