In the May 1980 issue of JMR, Lawrence replaces the gamma distribution on the purchasing rate component of the negative binomial model with the lognormal distribution. In this response the author shows that Lawrence's modeling effort is incomplete and that his data analysis is inconsistent with his implied model. In addition it is argued that the gamma distribution per se has some major advantages with respect to the lognormal distribution proposed by Lawrence.
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References
1.
ChatfieldC. and GoodhardtG. J. (1973), “A Consumer Purchasing Model With Erlang Inter-Purchase Times,”Journal of the American Statistical Association, 68 (December), 828–35.
2.
EhrenbergA. S. C. (1959), “The Pattern of Consumer Purchases,”Applied Statistics, 8 (March), 26–41.
3.
GreenwoodM. and YuleG. U. (1920), “An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings With Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents,”Journal of the Royal Statistical Society, 83, 255.
4.
HerniterJ. (1971), “A Probabilistic Market Model of Purchase Timing and Brand Selection,”Management Science, 18 (December), 102–12.
5.
JohnsonN. I. and KotzS. (1969), Discrete Distributions. New York: John Wiley & and Sons, Inc.
6.
LawrenceR. J. (1980), “The Lognormal Distribution of Buying Frequency Rates,”Journal of Marketing Research, 17 (May), 212–20.
7.
MorrisonD. G. (1969), “Conditional Trend Analysis: A Model That Allows for Nonusers,”Journal of Marketing Research, 6 (August), 342–6.
8.
MorrisonD. G. and SchmittleinD. C. (1980), “Jobs, Wars and Strikes: Probability Models for Duration,”Oranizational Behavior and Human Performance, 25 (April), 224–51.
9.
MorrisonD. G. and SchmittleinD. C. (1981), “Predicting Future Random Events Based on Past Performance,”Management Science, 27 (September), 1006–1023.
10.
SchmittleinD. C. and MorrisonD. G. (1980), “Prediction of Future Random Events with the Condensed Negative Binomial Distribution,”Research Paper 323A, Graduate School of Business, Columbia University.
