Some Results on the Non-Homogeneous Hofmann Process

Abstract

The classical counting processes (Poisson and negative binomial) are the most traditional discrete counting processes (DCPs); however, these are based on a set of rigid assumptions. We consider a non-homogeneous counting process (which we name non-homogeneous Hofmann process – NHP) that can generate the classical counting processes (CCPs) as special cases, and also allows modeling counting processes for event history data, which usually exhibit under- or over-dispersion. We present some results of this process that will allow us to use it in other areas and establish both the probability mass function (pmf) and the cumulative distribution function (cdf) using transition intensities. This counting process (CP) will allow other researchers to work on modelling the CP, where data dispersion exists in an efficient and more flexible way.