Estimating the Proportion of Always Buy And Never Buy Consumers a Likeliho

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Estimating the Proportion of Always Buy And Never Buy Consumers a Likeliho
Manohar U Kalwani
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Obviously a sample of 50 consumers with three purchases each is not sufficient to test if a proportion of the con- sumers in the population are "always buy" or "never buy" customers. On the other hand, a sample of 10, 000 consumers with 20 purchases is clearly adequate to test for spikes. It is not obvious what purchase sequence lengths and sample sizes are required to detect mass-points in purchase probability distributions. Also, it would be useful to know the trade-off between sample size an...d purchase sequence length requirements for detecting and estimating spikes.
-8- We determine these requirements through the use of simulated data. We generate samples from eleven different settings which extend over the spectrum of zero-order models. The first five settings are based on pur- chase probability distributions with no spikes. The probability distribu- tion is allowed to take various shapes like uniform, bell, "decay curve, " U and reverse J. These five settings are described in greater detail with the actual values of the parameters in a different paper by the authors (see Kalwani and Morrison [5]).


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