A useful discrete distribution (the Conway-Maxwell-Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway-Maxwell-Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway-Maxwell-Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway-Maxwell-Poisson distribution in fitting count data which do not seem to follow the Poisson distribution. Copyright 2005 Royal Statistical Society.

Most supermarket categories are cluttered with items, or stockkeeping units (SKUs), that differ very little at the attribute level. Previous research has found that reductions (up to 54%) in the number of low-selling SKUs need not affect perceptions of variety and therefore sales, significantly. In this research, the authors analyze data from a natural experiment conducted by an online grocer, in which 94% of the categories experienced dramatic cuts in the number of SKUs offered, particularly low-selling SKUs. Sales were indeed affected dramatically, increasing an average of 11% across the 42 categories examined. Sales rose in more than two-thirds of these categories, nearly half of which experienced an increase of 10% or more; 75% of households increased their overall expenditures after the cut in SKUs. In turn, the authors examine how different types of SKU reductions-defined by how the cuts affect the available attributes or features of a category (e.g., the number of brands)-affected purchase behavior differently. The results indicate that consumers experienced divergent reactions to the reduction in sizes, but they uniformly welcomed the elimination of clutter brought on by the reduction in redundant items. In addition, of households that were loyal to a single brand, size, or brand-size combination that was eliminated, nearly half continued purchasing within the category. Also, contrary to previous research on SKU reductions, the authors find that category sales depend on the total number of SKUs offered. The authors extend the previous research by showing that (1) category sales depend on the availability of key product and category attributes and (2) two particularly important attributes to consumers in an assortment are brand and flavor.

Huber, as well as the three anonymous JMR reviewers for their helpful comments. Both authors contributed equally.

T his research investigates the impact of a large-scale assortment reduction on customer retention, utilizing a model we develop to explore the effect on sales at both the store level and the category level simultaneously. We apply our model to a data set provided by an online grocer. The data contain detailed household purchase records for every category in the store. Our results indicate that the reduction in assortment reduces overall store sales, a result that contrasts with that of all of the recent studies on assortment reductions (Food Marketing Institute. 1993 Forthcoming). We find the reduction had a negative effect on both shopping frequency and purchase quantity, and we find that the decline in shopping frequency resulted in a greater loss than did the reduction in purchase quantities. We also find that the impact of the assortment cut varies widely by category, with less-frequently purchased categories more adversely affected. The variation in the assortment reduction's impact across categories suggests that managers compare select categories in order to moderate the overall loss in sales.

Entertainment marketing, Motion picture distribution and exhibition, Movie choice, Predictors, Influencers, Wide-release, Platform-release, Movie critics, Stochastic variable selection, Bayesian models, New product research, C01, C11, C52, M31,