Measuring an Equivalency about Purchasing Intervals Based on the Gini Index
Hiroyasu Abe1, Yoshikazu Terada2, Hiroshi Yadohisa3
1Graduate School of Culture and Information Science, Doshisha University, Kyotanabe, Kyoto, Japan; 2Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan; 3Department of Culture and Information Science, Doshisha University, Kyotanabe, Kyoto, Japan

In recent years, one to one marketing has been attracting much attention in various marketing fields. The concept of the marketing is establishing and keeping a company's interaction for each customer by knowing the characteristics and the needs of customers.

In the approach, we need to collect data about customer's preferences, such as buying history data, and analyze them for customer evaluations.There are many indexes of customer evaluations for one to one marketing.For example, Abe and Kondo (2005) proposed the survival probability of an individual customer based on a consumer behavior model.

In this paper, we propose a new method for evaluating customers in terms of purchasing intervals based on the Gini index. By using this method, we can evaluate how regular intervals the customer have purchased at.

To measure an equivalency about purchasing intervals, we calculate the Gini index using the data of the time length of the purchasing intervals with a customer. If the Gini index is near to 0, the customer purchased at regular intervals. On the other hand, if it is near to 1, the customer purchased at irregular intervals.

However, there are two problems when we measure equivalency about purchasing intervals by using the Gini index. One problem is that the time lengths from first purchasing to newest purchasing or the number of purchasing intervals make the max value of it different. We solved this problem by using the modified Gini index that is the standardized Gini index with max value of it. The other problem is that we cannot measure the local equivalency about purchasing intervals by using the Gini index with the all past data. To calculate it, we set the time frame which is shorter than the time length of observing and we calculate the Gini index using the purchasing data in the time frame. This approach enables us to derive the time series graph with the equality of purchasing intervals for each customer.

Bibliography:

Gini, C. (1912), Variabilita e mutabilita, Studi Economico-Giuridici dell'Universita di Cagliari, 3, 1-158.

Makoto, Abe. (2005), Counting Your Customers One by One: An Individual Level RF Analysis Based on Consumer Behavior Theory, Discussion Paper F series (CIRJE-F-408), UT Repository, The University of Tokyo.

Peppers, D. and Martha, R. (1993), The One to One Future, Currency Doubleday.

Keywords: Customer Relationship Management; One to one marketing; Customer base analysis

Biography: Master course student of Graduate School of Culture and Information Science, Doshisha University, Japan.