The probabilities , ,  and  can be modeled is a form such that one can easily use the concept of Markov matrix to answer many of the queries which are very much relevant for the marketing firm or the company. One can possible use the Erlang or the Poisson processes to denote the purchase time process of the customer.

One should remember that what is of interest is the fact that the marketing firm or the company wants to characterize the distribution of  over time, where this is given by ,.and , ,.. are the Erlang processes with parameters  and  (which is a positive integer). Consequently one can then assume that the distribution of  is Gamma with certain parameters which can be calculated using  and  (which have been mentioned above).

Finally if the marketing firm denotes   as the variable which signifies the number of time the product is purchased in the time interval, ,  then one can easily solve to calculate the expected fraction of the total market which purchases the product class . Using Dirichlet and Multinomial models one can furthermore study the choice process. Similarly using multiple hyper geometric models one can throw light on the concepts of integrated brand choice and purchase time model which may be of interest to the marketing firm as well as to the company at large.