Simple models for macro-parasite distributions in hosts

The Negative binomial distribution is the most used distribution to model macro-parasite burden in hosts. However, reliable maximum likelihood parameter estimation from data is far from trivial. No closed formula is available and numerical estimation requires sophisticated methods. Using data from the literature, we show that simple alternatives to negative binomial, like zero-inflated geometric or hurdle geometric distributions, produce in some cases a better fit to data than the negative binomial distribution. We derived simple closed formulas for the maximum likelihood parameter estimators which constitutes a significant advantage of these distributions over the negative binomial distribution.