Poisson distribution

Poisson distribution

A Poisson distribution is a probability distribution used to count random events over a given period or area.1 Number of cars reaching the expressway in 1 minute or number of dead cells in 1 square millimeter.

How does the Poisson distribution relate to web writing?

-We can use the Poisson distribution to estimate the number of people using our website over some time. or the number of clicks that occur on a web page This will help us plan resource allocation. or analysis of user behavior

-We can use the Poisson distribution to simulate errors or failures of our website systems. This will help us to improve reliability. or dealing with crises

-We can use the Poisson distribution to create test data or mock data for developing our website. This will allow us to test its accuracy. or appropriateness of the code or design

Choosing the parameters of the Poisson distribution is important in analyzing count data. or the number of events that occur in a given period or area. However, choosing this parameter is not an easy task. This is because it depends on the nature of the data and the purpose of the analysis.

Several methods can be used to select the parameters of a Poisson distribution, e.g.

-Maximum Likelihood Estimation method, which is a method that tries to find parameter values ​​that make the probability of the data we have the highest value.

- Method of estimating parameters using moments (Method of Moments), which is a method that uses the expectation value and the variance of the data to find the parameter value.

-Method of testing the distribution parameters of the Generalized Poisson Regression Model, which is used in cases where the data has a distribution that is different from the Poisson distribution. Or is there a distribution that is higher or lower than the threshold? (Overdispersion or Underdispersion) using various statistical tests such as the Z test, Wald test, likelihood ratio test, score test, and Q test.

This method of selecting the Poisson distribution parameters has advantages and disadvantages. This depends on the nature of the data and the purpose of the analysis. Therefore, researchers should study and compare different methods. Before choosing any one method the appropriateness of the chosen method should be checked using statistical methods.