Provides functions for fitting discrete distribution models to count data. Included are the Poisson, the negative binomial, the Poisson-inverse gaussian and, most importantly, a new implementation of the Poisson-beta distribution (density, distribution and quantile functions, and random number generator) together with a needed new implementation of Kummer's function (also: confluent hypergeometric function of the first kind). Three different implementations of the Gillespie algorithm allow data simulation based on the basic, switching or bursting mRNA generating processes. Moreover, likelihood functions for four variants of each of the three aforementioned distributions are also available. The variants include one population and two population mixtures, both with and without zero-inflation. The package depends on the 'MPFR' libraries (&lt;<a href="https://www.mpfr.org/" target="_top">https://www.mpfr.org/</a>&gt;) which need to be installed separately (see description at &lt;<a href="https://github.com/fuchslab/scModels" target="_top">https://github.com/fuchslab/scModels</a>&gt;). This package is supplement to the paper "A mechanistic model for the negative binomial distribution of single-cell mRNA counts" by Lisa Amrhein, Kumar Harsha and Christiane Fuchs (2019) &lt;<a href="https://doi.org/10.1101%2F657619" target="_top">doi:10.1101/657619</a>&gt; available on bioRxiv.