About Probability Playground

The idea for Probability Playground came about while I was taking the Biostatistics MA program at the University at Buffalo. Classes in probability theory and statistics referred to over a dozen common probability distributions, their mass or density functions, their moments, and how to derive them. By the end of the first year I could work with these distributions algebraically, but still didn't have a intuitive feel for many of them. I was often left with the following unanswered questions:

  • What kinds of shapes can the graphs of the distributions take, and how do these shapes depend on the parameters?
  • How do the distributions arise naturally?
  • If one distribution converges to another distribution, under what circumstances is it a good approximation?
  • If one distribution is a special case of another, how do the shapes of their probability mass or density functions compare?
  • If one distribution is a transformation of another, how does it change as the shape of the other distribution changes?
  • If one distribution is derived from a sample of another distribution, how does its shape change as the sample size increases?

Probability Playground was designed as an interactive tool for answering these questions and for exploring the most common (and some not-so-common) probability distributions and their relationships to each other. The design philosophy focuses on developing intuition through exploration. It uses web technologies such as JavaScript and D3 graphics to implement several novel features, including:

  • An intuitive interface for exploring the shapes of twenty-nine probability mass and density functions.
  • Both automatic and manual control over axis scaling.
  • Dynamic loading of examples illustrating the range of shapes distributions can take.
  • Interactive exploration of the relationships between distributions through transformation of variables, summing variables, sampling, and limiting distributions.
  • Interactive visualizations of the processes generating each distribution.

Probability Playground also provides proofs for the mean and variance of each distribution and over 100 proofs for the relationships between distributions. I hope it's useful to you, and would welcome any comments, suggestions for improvement, or compliments!

Publicity and Awards

  • A paper on Probability Playground was accepted for the conference JSM 2023 and published in October 2023: "Probability Playground: Exploring Probability Distributions through Interaction". This gives a detailed description of what the website does and how it was developed.
  • This paper won the Best Contributed Paper Award in the Statistics and Data Science Education Section at JSM 2023. The award has been given annually since 1988, and is selected based on audience evaluations.
  • The ASA Section on Statistics and Data Science Education highlighted Probability Playground in their BLOG, which gives a great summary of what the website does and how it was developed.
  • The Health Impact magazine of the University at Buffalo School of Public Health and Health Professions wrote a profile covering Probability Playground (pages 22-23).

Thanks!

Thanks to Eli and Indigo Fox, Matthew Morse, and Jon Rogers for testing and feedback.