# Poisson Distribution

##### Sarmistha ChakraborthyJul 11, 17

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or period.

1. Poisson Distribution
What is Poisson Distribution?
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or period.
This Distribution name has been consider on the name of French Mathematician Simeon Denis Poisson.

Attributes of a Poisson Experiment
A Poisson experiment is a statistical experiment that has the following properties:
1. The experiment results in outcomes that can be classified as successes or failures.
2. The average number of successes (mu) that occurs in a specified region is known.
3. The probability that a success will occur is proportional to the size of the region.
4. The probability that a success will occur in an extremely small region is virtually zero.
Hence, that the specified region could take many forms. For instance, it could be a length, an area, a volume, a period of time, etc.
Meaning of Poisson distribution
A statistical distribution showing the frequency probability of specific events when the average probability of a single occurrence is known. The Poisson distribution is a discrete function.
Use of Poisson distribution
If a mean or average probability of an event happening per unit time/per page/per mile cycled etc., is given, and you are asked to calculate a probability of n events happening in a given time/number of pages/number of miles cycled, then the Poisson Distribution is used.
For more you can use:- stattrek.com/probability-distributions/poisson.aspx
In Six Sigma we have Two types of Sample Poisson Tests
1. 1 Sample poisson rate (Use for Base line Identification and for validation)
2. 2 Sample poisson rate (Use for comparison of rate of occurrence between two samples)

How to use Minitab for these test

1. Sample poisson rate

Go to Stat>Basic stat>1-Sample Poisson Rate

Select Data from the box

We can see the Base line (95% CI)=(16.5405, 19.1828)

This base helps us to decide the next target for improvement

If we select the target here then it helps us for validation

P-Value>0.05, Ho (Null) is true, there is no significant impact on rate of occurrence

P- Value<0.05, Ha (Alternate) is true, there is a significant impact on rate of occurrence

Two Sample Poisson Rate

Go to Stat>Basic stat>2-Sample Poisson Rate

Select Data from the box

If we have 2 sample in two columns, then select the second option

P-Value>0.05, Ho (Null) is true, there is no significant impact on rate of occurrence

P- Value<0.05, Ha (Alternate) is true, there is a significant impact on rate of occurrence

Hence, there is a significant difference between the rate of occurrence of sample A and Sample B

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