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Uses of Poisson Distribution


The Poisson distribution is a discrete random distribution that can take all the non-negative integer values from zero to infinity. Poisson distribution can be used to explain the behavior of the discrete random variables where the probability of occurrence of the event is very small and the total number of possible cases is sufficiently large. As such Poisson distribution has found application in a variety of fields such as Queuing Theory (waiting time problems), Insurance, Physics, Biology, Business, Economics, E-commerce, and Industry.

Most of the Temporal Distributions (dealing with events that are supposed to occur in equal intervals of time) and the Spatial Distributions (dealing with events that are supposed to occur in intervals of equal length along a straight line) follow the Poisson Probability Law. We give below some practical situations where Poisson distribution can be used :

  1. The number of telephone calls arriving at a telephone switchboard in unit time (say, per minute).
  2. The number of customers arriving at the supermarket per hour.
  3. The number of defects per unit of manufactured product. This is done for the construction of a control chart for the number of defects in Industrial Quality Control.
  4. To count the number of radioactive disintegrations of a radio-active element per unit of time (Physics).
  5. To count the growth of the number of bacteria per unit of time (Biology).
  6. The number of defective materials say, pins, blades, etc. in a packing manufactured by a factory.
  7. The number of suicides reported on a particular day or the number of causalities (persons dying) due to a rare disease such as heart attack or cancer or snake bite in a year.
  8. The number of accidents taking place per day on a busy road.
  9. The number of typographical errors per page in a typed material or the number of printing mistakes per page in a book.


Business Statistics – SC Gupta and Indra Gupta

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