A note on the exponential Poisson distribution: A nested EM algorithm

An EM type algorithm for estimating the parameters of the exponential Poisson distribution has recently been proposed. This algorithm uses a Newton Raphson approach at the M-step. An alternative approach, where the Newton Raphson step is replaced by another EM algorithm is described. This approach has simple closed form expressions, making use of a nested EM scheme where the M-step itself is solved with an EM algorithm. An advantage of this algorithm is that it provides estimates in the admissible range when the initial values are in the admissible range, and avoids overflow problems that may occur during Newton–Raphson iterations and, in certain cases, it can be faster. Some simulation evidence on the speed of the new approach compared to the one that uses Newton–Raphson is provided.