Poisson Distribution Test

Copying poisson

poisson is a program that allows you to have 100 poisson chances of success per batch or lapse of time. It is used in the datagen package to illustrate the chi-square test.

poisson has two parameters:

The program makes 100 attempts to succeed in each trial. The probability of success is the mean divided by 100. The probability of failure is one minus the probability of success. n equals 100.

Example of how to run the program.

      poisson 10000 2.0

In this example, the program tries to achieve a mean of 2.0, 10 thousand times, and then prints the probability distribution, the standard deviation, and the chi-square test.

The Chi-square number should fit within the Range 95 percent of the time.


References

The calculation of probabilities for the poisson distribution is based on the following book:

Lincoln L. Chao
Statistics for Management
2nd Edition
Palo Alto: The Scientific Press, 1984
Chapter 7, Discrete Probability Distributions
Section 4, Poisson Distribution

Lincoln L. Chao published his book while at California State University, Long Beach.

The chi-square test is similar to:

Chapter 12, Chi-square Tests
Section 3, Testing for Goodness of Fit
Formula 12-3
Example 12-4

In Table 12-3, each category in the chi-square test has a different expected frequency. This corresponds to the different expected frequencies for the number of successes.