Poisson Distribution

Introduction

Poisson Distribution is an important statistical concept that is defined as a theoretical discrete distribution of probability and Poisson probability distribution of mass function. This distribution is particularly utilized for finding the probability of a specific independent event whose occurrence is continuous within a fixed time interval and the mean rate is constant. This mass function of a Poisson probability distribution can also be utilized in various other types of fixed intervals like distance, area, volume, etc. A random variable within the Poisson distribution will help in describing a particular phenomenon if the number of successes is less in comparison to the huge number of trials. Poisson distribution can also be regarded as binomial distribution’s limiting case. 

Poisson distribution Definition

Poisson distribution definition can be used as a model for analyzing the discrete probability for a particular event whose occurrence is continuous within a fixed time interval and the mean rate is constant. In simple words, the distribution of Poisson is used for predicting the number of times an event will occur within a specific period. The main parameter utilized in Poisson distribution is λ. It shows the expected value of the mean number of events within a given time interval. The distribution by Poisson is widely used in several areas of biology and business. 

For instance, let us consider a call center receives around 50 calls per half hour for 8 hours within a day. Here it can be easily noticed that the calls do not depend on each other. Hence, the probability of receiving the total number of calls within a minute is given by the probability distribution by Poisson. In this context, it should be mentioned that the number of calls taken in a minute can be anything and does not depend on the number of calls taken at the last minute. 

Poisson distribution formula

Poisson distribution formula is particularly used for finding the probability when the number of times for which the event is happening is known. In simple words, the formula helps in identifying the number of times an event will occur within a given time duration. The random variable in Poisson distribution denoted by “x” is utilized for denoting a total number of successes within an experiment. The Poisson distribution normally models the overall independent events within the specified interval of time. 

For a Poisson variable that is random like y = 0, 1, 2,…., ∞ the formula for Poisson distribution is given by f (y) = P(Y = y) = e–λ λy / y! where

• y is the random variable in Poisson distribution giving the total number of occurrences as y = 0, 1, 2, ….
• e is denoted as the number of Euler and its value is 2.71828
• ! denotes the factorial of the random variable.
• λ is denoted as the mean value rate within the desired interval of time.

In short notation, the possion distribution formula is shown as Y ~ P(λ).

Poisson distribution Calculator

Poisson Distribution Calculator is an online as well as a free tool for calculating the probability of occurrence of a particular event in Poisson distribution. Several online platforms and sites provide a Poisson distribution calculator. This calculator shows the value of probability for a provided success rate as well as the random variable in the Poisson distribution. Using an online Poisson distribution calculator is quite easy. However one must have some prior knowledge regarding different aspects of a Poisson distribution. 

The procedures for using different types of Poisson distribution calculator is almost the same with slight slight differences. The steps for properly using a Poisson Distribution calculator have been outlined in the following. 

• Firstly, enter the random variable of Poisson distribution and the average success rate in the appropriate input fields. 
• Secondly, click on the button on which solution is written to obtain the value of probability.
• After clicking, the value of probability through the use of the Poisson distribution will be displayed within the field of output.

Calculating the probability within the Poisson distribution can take some time, but with the help of the Poisson distribution calculator, it can be done within seconds.

Conclusion

Throughout the article, the statistical topic of Poisson distribution has been discussed in detail. Carrying out the calculation of the probability of different independent random variables according to the Poisson distribution is quite important in Agriculture engineering. To analyze the main topic several subtopics have been discussed namely the Poisson distribution definition, Poisson distribution formula, and the Poisson distribution calculator.