Summary
Summary Poisson distribution
- Course
- Statistics (STK220)
- Institution
- University Of Pretoria (UP)
A brief overview of the Poisson distribution.
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Poisson distributionA Poisson distribution is a tool that helps to predict the probability of a given number of
events happening in a fixed interval of time. Because of this application, Poisson
distributions are used by businessmen to make forecasts about the number of
customers or sales on certain days or seasons of the year.
The first 3 properties are the similar to the properties of the binomial distribution
Poisson then added property 5 & 6 in order to make it a Poisson distribution
Property 5 states that if the number of trials were large and the probability of a
success is small (5%</) due to the large trials
Property 6 states that the expected value/mean of the limiting conditions/Poisson
can be regarded as a constant (lambda)
Basically a binomial distribution with large number of trials can be
approximated by the Poisson distribution, only if the mean is constant
, 1. Number of trials are greater than or equal to 20 or 100
2. The probability of a success is small or equal to 5% or smaller than
10%
λ is the shape parameter which indicates the average number of events
e is the base of the logarithm
x is a Poisson random variable
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