Some properties of the 'Hermite' distribution

An application of compound Poisson modelling to biological dosimetry

“…These distributions have been reported by several authors, the case r = 2 by Kemp & Kemp (1965), the two-parameter generalization by Gupta & Jain (1974) and the generalized rth-order univariate used in this paper by Milne & Westcott (1993). However, in practice, these distributions have not often been used.…”

“…Notice that when r = 1, the pgf of the Poisson distribution is obviously obtained. When r = 2, the pgf in equation (2.2) corresponds to the Hermite distribution (Kemp & Kemp 1965, 1966. For r > 2, Milne & Westcott (1993) call these distributions Generalized Hermite or rth-order univariate Hermite.…”

An optimal bivariate Poisson field chart for controlling high-quality manufacturing processes

“…In Chiu and Kuo (2008), Chiu and Kuo presented their chart which is based on the exact distribution of sum of multivariate Poisson variables. By Hermit distribution which was presented as the special case of Poisson ''doublet" variables in Kemp and Kemp (1965), the exact distribution of sum of bivariate Poisson variables (SUMMTP) is:…”

Webbing clothes moth catch and the management of heritage environments

“…It has a probability mass function described by the formula: It has proved especially useful in describing shipboard epidemics, banking crises (Giles, 2010) and agricultural outbreaks of insects (e.g. Kemp and Kemp, 1965). It would seem a good choice although it can take on a multimodal character.…”