A Poisson Distribution and Central Limit Theorem App!

Peijin Chen
April 5, 2017

Introduction: Poisson Sample and Central Limit Theorem Explorer

This is a Shiny app for allowing students to simulate and visually understand the Poisson distribution using a sample size and a mean/variance parameter of their own choosing.

The Poisson Distribution

Many fundamental distributions of random variables have shapes that change drastically depending on their parameters. This app allows someone to play around with those parameters and see how the shape changes. This is based on simulation or random selection of Poisson variables,whose distribution/density are then plotted, resulting in something like the following:

plot of chunk plots

The Central Limit Theorem

Changing the parameters and sample size of the random Poisson variables allows one to see if the Normal approximation of the Poisson–which follows from the Central Limit Theorem– really “works”. The parameters are chose using two slider inputs.

How Normal Is It?

Another facet of the app is that you can (visually) check how close the simulated series is to a normal curve using the QQ plot, to see how far it deviates from true normality. For example, one might see something like the following:

plot of chunk qq

Conclusion

This App and others like it could be a useful interactive tool in teaching people some of the basics of statistical theory.