Mathematical Calculators

Poisson Distribution Calculator

The Poisson distribution calculator will allow you to determine the likelihood of an event occurring a number of times during a certain time frame.

Poisson Distribution Calculator

P(X = x) = e • λx / x!

Table of contents

What is the Poisson distribution?
Poisson distribution examples
When is it not appropriate to use the Poisson distribution

What is the Poisson distribution?

The Poisson distribution can be described as a probability distribution. It is similar to the binomial. It indicates the probability that a specific number of events will occur over a period of time. You can use past data to calculate this probability and find out about the frequency of events.
Consider, for instance, that the average number of tornadoes in a region over ten years has been 5. This allows us to calculate the probability there will not be any tornadoes in the area over the next ten-year period. The probability of any other tornadoes developing in this area during the next ten-year period can also be calculated.

Poisson distribution examples

These are just a few examples of events that you can analyse with the Poisson distribution calculation calculator:
Number of buses arriving at a bus station per hour
In a sample of 1,000 photos, the number of blurred images is
The number of meteors that have struck the Earth in the past 100 years.
How many times a student has been absent from school during the schoolyear;
The number of people visiting a museum between 10 and 11 o'clock in the morning.
The Poisson distribution can be used to identify events that are independent of each other. Their probability doesn't change over time. These events could be described as accidental, but they are inevitable. For example, a bus arrives 20 minutes late only to have two buses arrive simultaneously.

When is it not appropriate to use the Poisson distribution

A discrete distribution like the Poisson is an example. The Poisson distribution table can only be used for integer arguments. Contrary to continuous distributions, such as normal, which may take any value, the Poisson distribution table can only assume a countably infinite number.
Additionally, the Poisson distribution calculation calculator is not to be used when
Events can't be separated (probabilities of future events could change over the course of time);
It is unlikely that an event will occur (probability function undefined for zero events).
The Poisson probability formula does not work correctly in this first case if events are repeatedly correlated. There are many examples of positive autocorrelation within the data. For example, a volcano eruption can make other volcanoes less likely to erupt. Or an epidemic disease with high dynamics.
When we have to deal with events where zero is not possible, the Poisson distribution needs to be enhanced. For example, patients who are hospitalized must never leave the clinic after zero days. This problem can be solved using trimmed Distributions such as The zero-truncated Poisson Distribution which only uses a set of positive integers.

Parmis Kazemi
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Parmis Kazemi
Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things.

Poisson Distribution Calculator English
Published: Wed Jun 08 2022
In category Mathematical calculators
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