Pareto and Parameters: How Customer Concentration Varies with NBD Parameters

Abstract

The Pareto Effect is known as a “rule of thumb” whereby the top 20% of a category’s customers account for a disproportionate percentage of the category’s turnover. The precise manner of the variation has not been clear. In considering how the Pareto Share varies with both the A and K parameters of the category’s Negative Binomial Distribution (NBD), this paper proposes a structure whereby Pareto Share varies in a predictable manner. The motivation for this investigation came from an initial analysis of one year’s purchase data for six categories of wine product where the Pareto Share appeared to vary in a manner that was counter-intuitive. Pareto Share is proposed to decrease with the category’s homogeneity (K) parameter, but along different lines, according to that category’s scale (A) parameter. This structure explained the mildly surprising result that the category (fortified) with the lowest measure of homogeneity (lowest K) also had the lowest Pareto Share. When considered on a large scale the difference in Pareto response due to A appeared negligible; it was only when we considered over a narrower operating range of K that the variation due to A became apparent.