A common problem in count data models is the over-dispersed quantities of purchase that can plague the model with severe skewness. The traditional method of either censoring or truncating, though may help to avoid part of extreme values, would still pay the cost of losing observations and thus reduce estimation efficiency. Because data on quantities purchased are discrete and over-dispersed and because demands of different brands may be correlated, we specify an approach that uses the multivariate Possion-log normal distribution in an incomplete demand system so that estimation on consumer’s brand choice can be accomplished without information loss.