Data Product Course Project - Pitch Presentation

Gamma Probability Density Function Plot

JC99

This project presents an interactive display that plots a gamma probability density function.

plot of chunk unnamed-chunk-1

Sliders provide an opportunity for the user to modify the function's shape and mean parameters (alpha and tau, respectively), with the plotted function changing accordingly.

The x-axis is scaled such that for a given value of tau, the range of the plotted function does not change as alpha is changed. The y-axis is scaled according to the maximum value of the function. Thus for a given value of alpha, the apparent shape of the function does not change as tau is changed (although the scales of both the x- and y-axes do change).

Some interesting trivia:

The gamma pdf is a more general form of the equation for the ideal response of some number of equally-sized completely-mixed "tanks" arranged in series, to instantaneous input of an inert tracer. In such a circumstance the "shape" parameter alpha equals the number of such tanks, and the "mean" parameter tau equals the system's mean residence time. While the number-of-tanks is necessarily an integer property, the alpha parameter need not be. A surprising number of environmental transport phenomena (besides reactors in series) can be reasonably well characterized with gamma pdfs.