Randomly stopped models

We introduce a method for modelling a continuous response which is the sum of a random number of terms. Examples are total insurance claim sizes (the total of all claims on a policy in a year), or total amount spent by credit card holders in a sector in a month, where there may be multiple spending episodes. The distribution of the number of terms may be, in principle, any discrete distribution defined on the non-negative integers; and each term has a continuous, right-skewed distribution. The resulting marginal distribution of the total amount is a mixed discrete-continuous model, with a probability mass at zero and a continuous component. The model explicitly specifies log-linear models for the four parameters in the total amount distribution. It may be fitted to data using a package written in R. The method is illustrated on an Australian motor vehicle insurance data set.