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Abstract
The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. This paper provides the second part of the list of approximate forms for the compound mixed Poisson distribution (following up from Nadarajah and Kotz (Citation2006)). The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science.