Some properties of the inhomogeneous panjer process

The classical processes (Poisson, Bernoulli, negative binomial) are the most popular discrete counting processes; however, these rely on strict assumptions. We studied an inhomogeneous counting process (which is known as the inhomogeneous Panjer process-IPP) that not only includes the classical processes as special cases, but also allows to describe counting processes to approximate data with over-or under-dispersion. We present the most relevant properties of this process and establish the probability mass function and cumulative distribution function using intensity rates. This counting process will allow risk analysts who work modeling the counting processes where data dispersion exists in a more flexible and efficient way.