A stochastic model of consumer purchase behavior for frequently purchased, low cost products is developed. Both brand selection and purchase timing are incorporated in the model; a first-order Markov process is used to describe brand selection, and Erlang density functions are used to describe time between purchases. The market's behavior is obtained by describing the individual consumer's behavior and then aggregating over consumers. The model's predictions of various aggregate purchase timing statistics and repeat purchase sequences are empirically verified.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Marketing Association is collaborating with JSTOR to digitize, preserve and extend access to A probabilistic model of consumer purchase behavior for frequently purchased, low cost items is presented. The concept of maximum entropy is used to specify the model. The only empirical data required are market shares; all other brand selection statistics, such as repeat and switch rates, are derived quantities. AnEntropy Model o f Brand Purchase Behavior ENTROPY CONCEPTIn this article a probabilistic model of consumer purchase behavior for frequently purchased, low cost items is presented. The model is completely determined by specifying only the market shares; all other brand selection statistics, such as repeat rates and switch rates, are derived from the model. The model presented is a heterogeneous multinomial preference model. It is assumed that each consumer has a set of preferences for the brands in the market, and there is a distribution of the preferences over the population. The probability of a consumer purchasing a particular brand is numerically equal to her preference for the brand. Rather than specifying the joint distribution of preferences and fitting the parameters to empirical data, the concept of entropy is employed and the distribution is selected that maximizes the entropy of the system subject only to the empirical market share values. In this way the model developed differs fundamentally from the probabilistic market models previously published [1, 3, 7].In the physical sciences, where it was first introduced, entropy is considered a measure of the degree of disorder, uncertainty, or randomness of a probabilistic system. It is assumed that at equilibrium all probabilistic systems will be at the maximum entropy consistent with the constraints on the system. In the early work in statistical thermodynamics, the entropy equations are derived from the likelihood function for the system, and maximum entropy is completely equivalent to the maximum likelihood estimate. A second interpretation of entropy is by Jaynes [4] who writes:"Just as in applied statistics the crux of a problem is often the devising of some method of sampling that avoids bias, our problem is that of finding a probability assignment which avoids bias while agreeing with whatever information is given. The great advance provided by information theory lies in the discovery that there is a unique, unambiguous criterion for the 'amount of uncertainty' represented by a discrete probability distribution, which agrees with our intuitive notions that a broad distribution represents more uncertainty than does a sharply peaked one, and satisfies all other conditions which make it reasonable." This meas...
Simple Markov processes appear to provide a fruitful conceptual basis for study of customer populations in the face of marketing activity. The purpose of this paper is to summarize characteristics and some implications and applications of the Markov model. Characteristic behavior of the model is compared with published data, and areas for further analytical and experimental effort are indicated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.