35. Poisson Distribution

  1. Catherine Forbes1,
  2. Merran Evans1,
  3. Nicholas Hastings2 and
  4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch35

Statistical Distributions, Fourth Edition

Statistical Distributions, Fourth Edition

How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Poisson Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch35

Author Information

  1. 1

    Monash University, Victoria, Australia

  2. 2

    Albany Interactive, Victoria, Australia

  3. 3

    Brian Peacock Ergonomics, SIM University, Singapore

Publication History

  1. Published Online: 16 DEC 2010
  2. Published Print: 29 NOV 2010

ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242



  • parameter estimation;
  • Poisson distribution;
  • probability density function;
  • random number;
  • variate


The Poisson distribution is applied in counting the number of rare but open-ended events. A classic example is the number of people per year who become invalids due to being kicked by horses. Another application is the number of faults in a batch of materials. It is also used to represent the number of arrivals, say, per hour, at a service center. This number will have a Poisson distribution if the average arrival rate does not vary through time. If the interarrival times are exponentially distributed, the number of arrivals in a unit time interval is Poisson distributed. This chapter illustrates probability density function and distribution function for the Poisson variate. It discusses variate relationships, parameter estimation and random number generation for the Poisson variate.

Controlled Vocabulary Terms

control variate; Poisson distribution; probability density function