Estimating the Likelihood of

Estimating the Likelihood of Purchase



At the heart of our method for predicting consumer behavior is what we call the likelihood function. The function estimates the likelihood (Li) that a customer or household (i) will purchase a given product at a given time:



where:



Ri is the number of interpurchase times for customer or household i



if the ri th interpurchase time extends

beyond the observation window

otherwise



if product j is bought by customer or household i at time t; the probability that ijt =1 is Pij (t)

otherwise; the probability that ijt = 0 is (1—Pij (t))



and ƒi (•) and Si (•) denote the density and survivor functions, respectively.