An algorithm is proposed that, starting from the probability generating function of a lefttruncation at k of a mixed Poisson distribution, recovers the first k + 1 probabilities of the untruncated distribution, without the need of eliciting what the mixing distribution is. The result establishes that irrespective of the value where the distribution is truncated, there still remains enough information in the tail so that the initial mixing distribution can be recovered. (C) 2014 Elsevier B.V. All rights reserved.
Maceda (1948) characterized the mixed Poisson distributions that are Poisson-stopped-sum distributions based on the mixing distribution. In an alternative characterization of the same set of distributions here the Poisson-stopped-sum distributions that are mixed Poisson distributions is proved to be the set of Poisson-stopped-sums of either a mixture of zero-truncated Poisson distributions or a zero-modification of it.