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.
