Further results of recursive evaluation for compound distribution with the severity distribution of mixed type

Yang et al. [J.P. Yang, S.H. Cheng, Q. Wu, Recursive equations for compound distribution with the severity distribution of the mixed type, Science in China Series A 48 (2005) 594–609] investigated a recursive procedure for a kind of compound distributions with the number of claims belonging to (a,b)(a,b)-family and the severity distribution of the mixed type. In this paper, we extend their results by assuming that the claim number belongs to a larger class. As applications, the excess-of-loss reinsurance treaty is discussed and concrete examples are considered in some detail.