EM algorithm for an extension of the Waring distribution

The extended biparametric Waring (EBW) distribution is a useful model for overdispersed and underdispersed count data. When its first parameter α is positive, the EBW is a particular case of the univariate generalized Waring distribution, so it inherits its main properties, in particular, its expression as a Poisson mixture and hence the decomposition of the variance as a combination of three components (randomness, liability, and proneness), which make it of great interest. In this paper, we take advantage of the first property to obtain the maximum likelihood (ML) estimates of the EBW parameters by the expectation‐maximization algorithm. This algorithm, for mixed distributions, reduces the problem of ML estimation to one of ML estimations of the mixing distribution, which is usually easier.