Using Gemini for Statistics Apps
Sampling from Distributions
Building a Shinylive app with Gemini.
can you help me build a shiny app for statistical distributions? I want it to contain a drop down for sample sizes of 15, 30, 50, 100 and to include a drop down of distributions including the normal, binomial, geometric, poisson, uniform, and lognormal distributions. Responsive to the choice of distribution, parameters should be fields to be entered by the user. Once the user has made choices it should produce a table of summary statistics including the mean, standard deviation, and five number summary, and a histogram of the data.
Main page for the Statistical Distributions App created in Shinylive by Gemini.
Now I want to go back to the app and overlay a density plot and make the number of bins for the histogram a slider
Updated version Statistical Distributions App created in Shinylive by Gemini.
This is great. One more thing, I forgot the negative binomial distribution, please add it to this final app
Almost final version Statistical Distributions App created in Shinylive by Gemini.
This app is excellent. But it occurred to me that instead of the density, it should include either the theoretical pdf/pmf for the type of variable, best for seeing the differences between small and infinite samples.
Response
This is a fantastic pedagogical improvement. You are completely right: overlaying a theoretical density curve on top of a 15-sample histogram can actually be visually confusing.
To best illustrate the Law of Large Numbers (small sample vs. infinite sample), we should plot them side-by-side.
In this updated version:
The left plot is strictly your empirical data (the small sample histogram) plotted as actual counts/frequencies.
The right plot is the pure theoretical PDF (Continuous) or PMF (Discrete), representing the “infinite” sample.
Crucially, I wrote a logic block to lock the X-axes of both plots to the exact same scale. This means if your 15-sample misses the “tails” of a normal distribution, the histogram’s axis will stretch to match the theoretical plot, making the visual comparison perfectly 1-to-1.
Almost almost final version Statistical Distributions App created in Shinylive by Gemini.
Add the density plot overlay back on to the histogram please. I like the side-by-side but it mitigates the distortions of bin sizes for quantitative variables.
Final version Statistical Distributions App created in Shinylive by Gemini.