Art of Stat: Distributions3.0.0

News: The Distributions app is now part of the all new "Art of Stat" app, which contains this and seven other modules.

Please consider getting the Art of Stat app for the latest updates and features from the App Store. Simply search for "Ar of Stat" on the App Store. This app will continue to work, but future development is concentrated on the new Art of Stat app.

Original Description:
The Art of Stat: Distributions app explores and visualizes continuous and discrete probability distributions via sliders and buttons.

Don't rely on boring and complicated graphing calculators that don't deserve their name. Instead, use the interactive graphics that this app provides to learn about probability distributions and visualize results side-by-side with the numerical solutions.

Find probabilities or percentiles (two-tailed, upper tail or lower tail) for computing P-values or when working with discrete distributions. Obtain critical values for confidence intervals. Display the expected value and standard deviation, and simulate random numbers.

The app works in offline (airplane) mode and indicates this by changing the background color.

Continuous Distributions implemented so far:

- Normal
- Student's t
- Chi-Squared
- F
- Exponential
- Uniform
- Gamma
- Beta

Discrete Distributions:
- Binomial
- Geometric
- Poisson
- Define Your Own Discrete Distribution, or choose from preloaded examples, such as Benford's Distribution of the leading digit

Version History - Legacy Version: Continuous to work, but I recommend upgrading to the new "Art of Stat" app, which contains this and 7 other modules for one powerful app.
- Search for "Art of Stat" in the App Store. 3.0.0 Feb 4 - maintenance to keep everything running smoothly 2.6.0 09/09/2025 Finally: Better support for tablets and landscape mode. 2.5.0 09/10/2024 - Switch to enter numerical value for discrete distribution parameters (e.g., p or lambda) on Explore Distribution screen 2.3.0 03/01/2024 - Gamma Distribution
- Beta Distribution
- Simulate random numbers from distributions
- Specify your own discrete probability distribution 2.0.0 02/16/2023 - User-Specified Discrete Probability Distribution (plus Examples)
- Exponential Distribution
- Uniform Distribution 1.9.0 05/12/2022 - Discrete Probability Distribution
- Exponential Distribution
- Uniform Distribution 1.8.0 05/04/2022 - New icons for distributions on landing page
- Simulate random numbers
- Visualize simulated numbers in a histogram
- Compare the mean and standard deviation of the simulated numbers to the theoretical mean and standard deviation
- Help text now includes formulas & properties for distributions 1.7.0 01/24/2022 New Features:
- Simulate random numbers from the normal, Binomial, Geometric or Poisson distribution on a new tab called "Random Numbers"
- Visualize the simulated numbers in a histogram
- Compare the mean and standard deviation of the simulated numbers to the theoretical mean and standard deviation

Improvements:
- Better structure of the help text that describes all features of the apps when pressing the question mark symbol in the upper right corner
- Help text now includes new section on "Formulas & Properties", describing special features of each distribution and its use in inference. 1.6.0 10/05/2021 - Explore Binomial Distribution: Now enter a value for the sample size n as large as n = 1000 and use the slider for p to explore how the shape changes.
- Improved responsiveness of sliders and graphs
- When entering into offline mode, the background of the app's title turns green. 1.4.0 09/07/2021 The app now works in offline mode. No internet connection necessary. 1.3.0 07/16/2021 1.2.0 06/30/2021