Pitch Presentation for Gamma PDF Plotting Tool

Sliders are provided for the distribution's shape and mean parameters (referred to here as “alpha” and “tau”, respectively), with the plotted function changing in real time as new values for these are selected by the user.

The code for the tool may be found at:

https://github.com/JimC99/DataProductsCourseProject.

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 (possibly useless) trivia:

The gamma pdf is a generalized form of the equation for the ideal response of some number of equally-sized completely-mixed “tanks” (or reactors) 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.