etermination of Moments of Binomial Mixtures Using Recursive Relations

Abstract

Mixed distributions are important in modeling data whose distributions are heterogeneous. However, determining their moments can be cumbersome due to the fact that their constituent distributions are different. This challenge can be addressed using the recursive relations which can be constructed through integration by parts technique. The objective of this study was to construct recursive relations of Beta- binomial mixtures through integration by parts techniques and use the recursive relation obtained to determine moments of the mixtures. The outcomes will be used to obtain mean and variances of the mixed distributions. These recursive equations are useful in insurance industry where they are applied in calculation of total aggregated claims.