A markov-chain model for multivariate magazine-exposure distributions

A multivariate magazine-exposure model that generalizes Danaher’s univariate model is developed. Let S_i be the number of issues of magazine/a person reads (S_i = 0, 1,…, k_i i = 1,…. m). My Markov-chain model considers both within- and between-magazine correlation with the result that S₁…, S_m are conditionally independent given the reading outcome for the first issue of each magazine. I am ultimately interested in modeling ST = S„ the total number of exposures a person has to a set of magazines, and I derive this from the model for the joint distribution of (S₁…, S_m). The proposed model is shown to give a significantly better fit to observed exposure distributions than the best currently known models. Finally, I obtain the asymptotic distribution of Sr, which can be used for advertising schedules with many magazines and has the benefit of being computationally much faster than my exact model.