A simple heuristic for obtaining pareto/NBD parameter estimates
- PDF / 218,863 Bytes
- 9 Pages / 439.37 x 666.142 pts Page_size
- 93 Downloads / 154 Views
A simple heuristic for obtaining pareto/NBD parameter estimates Pablo Marshall
# Springer Science+Business Media New York 2013
Abstract In an influential study, Schmittlein et al. (1987) proposed the pareto/negative binomial distribution (P/NBD) model to predict purchase behavior of customers. Despite its recognized relevance, this model has some drawbacks as follows: (1) it does not allow a zero transaction rate, (2) it assumes convenient but not necessarily realistic gamma distributions for the transaction and drop-out rates across customers, and (3) the estimation procedure requires complicated computations. The purpose of this study is to relax the assumption that purchases and drop-out rates are distributed according to a gamma distribution and propose a simple estimation procedure for the individual parameters that can be applied even if the number of customers is large. A simulation exercise and empirical applications to real datasets compare the simple model proposed with the P/NBD model. The results show that the simple procedure is better in cases where the number of transactions and/or the observation period is large. Keywords Prediction consumer behavior . Nonparametric model . Pareto NBD model
1 Introduction The need to understand customer behavior and the interest of managers to focus on customers who can deliver long-term profits has changed the main purpose of marketers’ activities from acquisition to retention. Many companies, nowadays, face a database containing information on the frequency and timing of transactions for a list of customers, for the purpose of forecasting their future purchasing behavior at the individual level. Manager decisions oriented to the growth and retention of customers are usually based on these predictions. In an influential study, Schmittlein et al. (1987) proposed the pareto/negative binomial distribution (P/NBD) model to analyze and predict the purchase behavior of customers at the individual level in a non-contractual scenario. Under a non-contractual P. Marshall (*) Escuela de Administración, Pontificia Universidad Católica de Chile, Av Libertador Bernardo O Higgins 340, Santiago, Chile e-mail: [email protected]
Mark Lett
setting (e.g., retail store, supermarket, mail order), consumers do not declare that they have become inactive, but simply stop doing transactions with the firm. Thus, the time at which a customer becomes inactive is unobserved by the firm and the single evidence for this is an unusually long interval since the last recorded purchase. The challenge facing the analyst is how to differentiate between those customers who have ended their relationship with the firm from those who are in the middle of a long interval between transactions. The P/NBD model estimates the probability of being active and the expected number of future transactions for each customer. The model assumes that at time t=0 the individuals are active, and (1) while active, the number of transactions made by a customer follows a Poisson probability distribution, (2) the lifetime
Data Loading...
