Poisson distribution

What is Poisson distribution?
A Poisson distribution is generally defined as the tool to calculate the probability of the event when you know how often the event has occurred.
To explain in a simple manner, it gives the probability of the event generally happening in the fixed interval of time.

Attributes of Poisson distribution

  • The experiment results in the outcome that may be generally the success or failure.
  • The average numbers of success that are supposed to occur in the specified region are known clearly.
  • The probability of success is supposed to be proportional to the size of the region.
  • The probability of success to occur within the extremely small region is virtually zero.

The Formula for Poisson distribution
Mathematically, the Poisson probability is given by,
P(X;µ) = (e)(µ×)/x!
X = Generally the actual number of success that results from the experiment.
e = It is the constant approximately equal to 2.71828

Two Important Properties of Poisson Distribution
The mean of the distribution is generally equal to µ.
The variance is also given by µ.
The average number of homes sold by the XXX realty company is 2 homes per day on an average. What is the probability that 3 homes will be sold by tomorrow?
P(x; μ) = (e) (μx) / x!
P (3;2) = (2.71828-2)(23)/3!
           = (0.13534)(8)/6
P (3;2) = 0.180

The Need of the Poisson distribution
Poisson distribution is generally used to denote the probability for the rare events.

  • The number of defective pens per box of 5000 pens. 
  • The number of printing mistakes on each page while proofreading the book.

Graphical Representation of the Poisson distribution
All the Poisson distribution is generally skewed to right. This is the reason why Poisson distribution is called the probability of rare events.


Advantages of Poisson distribution

  • It generally has an infinite number of trials.
  • An unlimited number of outcomes is also possible.
  • It can be generally used to test the independence.
  • It can be used to predict the number of occurrences per unit, time and space.

Fitting the Poisson distribution

Generally, the process of fitting the Poisson distribution is very simple. We just need to obtain the m-value.
The list of other frequencies can be calculated by the below formula,
Po= Ne-m
P3=P2.m/3 etc…


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