Dirichlet Essay

340 Words2 Pages
The Dirichlet’s underlying assumptions Dirichlet is underpinned by two broad propositions. One concerns consumers and the other, brands. In the Dirichlet model customers are assumed to have steady propensities to buy any particular brand (different propensities for different brands). According to Sharp and Driesener (2000), the Dirichlet’s assumptions mean that the model applies to markets, which exhibit the following characteristics: * They are under stationary or “no trend” conditions and * The different brands show no special groupings, i.e. no market partitioning. Apart from those there are five distributional assumptions given by Goodhardt et.al. cited in Ehrenberg et.al.(2002). Two are about the product category: i. Each consumer is assumed to buy the category at some steady long run rate (e.g. once a month). ii. A consumer’s purchases of a category, are assumed to be spread irregularly over time and independently of when the previous purchase was made (a zero order process). The next two are about brand choice: iii. A consumer’s choice of a brand is independent of other irrelevant alternatives. iv. The probability of buying a brand on a particular occasion is independent of the brands the consumer has previously bought. And the final assumption is about the relationship between product category and brand choice: v. The distribution of brand choice probabilities is taken the same irrespective of the frequency of purchase by a consumer. Zero order process: A zero order process is one in which past behavior does not affect the future outcome. For example, in marketing, the zero order hypothesis holds that the brands you will purchase next will not depend on the brands you have purchased before. That means you have a fixed probability of purchase. NBD: Negative Binomial Distribution (NBD) theory is a mathematical model
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