In probability theory and statistics, the Geometric-Poisson distribution (another different version called the Pólya--Aeppli distribution,) is a combination both of the Geometric distribution and the Poisson distribution, and includes both of them as special cases.
In probability theory and statistics, the geometric Poisson distribution (also called the Pólya--Aeppli distribution) is a particular case of the compound Poisson distribution. It is a combination of the geometric distribution and the Poisson distribution, and includes both of them as special cases.