In the second part of this paper, we use the discrete MPH-distributions to model multi-variate insurance claim processes in risk analysis, where claims may arrive in batches, the arrivals of different types of batches may be correlated, and the amounts of different types of claims in a batch may be dependent. This provides one natural approach to model the dependencies among claim frequencies as well claim sizes of different types of risks, which is a very important topic in insurance risk theory. Under certain conditions, it is shown that the total amounts of claims accumulated in some random time horizon are discrete MPH random vectors. Matrixrepresentations of the discrete MPH-distributions are constructed explicitly. Efficient computational methods are developed for computing performance measures of the total claims of different types of claim batches and individual types of claims.