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keisanHigh-precision calculations for everyday life and work

Calculating the parameter K for the negative binomial distribution (NBD) model

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We calculate K—the parameter that determines the probability distribution in the negative binomial distribution (NBD) model, used in mathematical marketing to represent the probability of purchase frequency—using the Newton-Raphson method.
Reference: “Strategic Thinking Based on Probability: The Power of Mathematical Marketing, Proven at USJ” (Tsuyoshi Morioka, Seiki Imanishi)
Pen: Penetration rate (in %)
M: Average number of purchases per unit period (number of votes per person for the company’s brand within a given period)
Penetration Rate Pen
%
Average number of purchases per unit period M
Times
K 
There isn’t a solution for all values of Pen and M. See the graph above.
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