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.

Abstract
 1. INTRODUCTION
 2. A MIXTURE OF POISSON DISTRIBUTION HAVING GAMMA DISTRIBUTED RANDOM PARAMETERS WITH A FIXED TIME INTERVAL
 3. A MIXTURE OF POISSON DISTRIBUTION HAVING GAMMA DISTRIBUTED RANDOM PARAMETERS WITH A FIXED RATE PER UNIT TIME INTERVAL
 4. DISCUSSION
 REFERENCES

• Suneung Ahn(Hanyang University Department of Industrial Engineering)