The majority of papers on probabilistic inventory theory make the assumption that
the distribution of lead-time and demand are known, but this is unsupported in many
applied situations. In this paper, we present a theoretical support for the adoption
of the negative binomial distribution as an appropriate demand distribution in
retail inventory management. Used as a mixing distribution for an unknown Poisson
demand parameter, the gamma distribution leads to the negative binomial demand.
The hyper-parameters of the gamma distribution have different meanings according to
the sources of randomness in the Poisson demand parameter. Such two sources are lead
time and demand rate. Depending on the sources, we interpret the meanings of
the parameters. This paper presents appropriate inventory control interpretation
with parameter on fluctuating demand process.