Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application.

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application.

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application. We here assume that customer order sizes are described by the Poisson distribution with the random parameter following a gamma distribution. This implies in turn that the negative binomial distribution is obtained by mixing the mean of the Poisson distribution with a gamma distribution. The purpose of this paper is to give an interpretation of the negative binomial demand process by considering the sources of variability in the unknown Poisson parameter. Such variability comes from the unknown demand rate and the unknown lead time interval.

Used as a mixing distribution for an unknown Poisson parameter, the gamma distribution leads to the negative binomial distribution. The hyperparameters of the gamma distribution have their own meanings according to what the Poisson parameter represents. Different sources in the randomness of the Poisson parameter give different interpretations of the negative binomial distribution.