Generalized Hermite Distribution Modelling with the R Package hermite

The Generalized Hermite distribution (and the Hermite distribution as a particular case) is often used for fitting count data in the presence of overdispersion or multimodality. Despite this, to our knowledge, no standard software packages have implemented specific functions to compute basic probabilities and make simple statistical inference based on these distributions. We present here a set of computational tools that allows the user to face these difficulties by modelling with the Generalized Hermite distribution using the R package hermite. The package can also be used to generate random deviates from a Generalized Hermite distribution and to use basic functions to compute probabilities (density, cumulative density and quantile functions are available), to estimate parameters using the maximum likelihood method and to perform the likelihood ratio test for Poisson assumption against a Generalized Hermite alternative. In order to improve the density and quantile functions performance when the parameters are large, Edgeworth and Cornish-Fisher expansions have been used. Hermite regression is also a useful tool for modeling inflated count data, so its inclusion to a commonly used software like R will make this tool available to a wide range of potential users. Some examples of usage in several fields of application are also given.

David Moriña , Manuel Higueras , Pedro Puig , María Oliveira

CRAN packages used

maxLik, radir

CRAN Task Views implied by cited packages



Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".


For attribution, please cite this work as

Moriña, et al., "The R Journal: Generalized Hermite Distribution Modelling with the R Package hermite", The R Journal, 2015

BibTeX citation

  author = {Moriña, David and Higueras, Manuel and Puig, Pedro and Oliveira, María},
  title = {The R Journal: Generalized Hermite Distribution Modelling with the R Package hermite},
  journal = {The R Journal},
  year = {2015},
  note = {},
  doi = {10.32614/RJ-2015-035},
  volume = {7},
  issue = {2},
  issn = {2073-4859},
  pages = {263-274}