Compound Demand Distributions

This chapter begins by examining the properties of compound Poisson distributions, showing that they are more flexible than the (non-compound) Poisson distribution. The compound Poisson is actually a family of distributions, which restricts demand incidence to be Poisson but allows for any probability distribution of demand sizes. The chapter looks at the characteristics for two members of the compound Poisson family that have been recommended for intermittent demand, namely the stuttering Poisson distribution and the negative binomial distribution. The compound Bernoulli family of distributions has some attractive features. It is based on Bernoulli demand occurrence, which has a theoretical justification as a memoryless distribution. The compound Erlang distributions have a natural a priori justification as a ‘censored Poisson process’. The chapter discusses distributions that allow for more regular demand incidences than the compound Poisson, and may therefore act as a complementary family of distributions.