
Website of Randall J. Patton
Studies
Below are links to studies I have done on a range of topics, both during my working career and recently in retirement. Full discussion for each topic is contained in the linked PDF files.
Survival Modeling
This study was inspired by a friend's observation that, the longer a person was a member of a group, the more likely they were to stay in the group. The ensuing analysis revealed a general technique for generating important probability distributions associated with survival modeling.

Breaking the Sound Barrier
Felix Baumgartner broke the sound barrier in 2012 by jumping out of a balloon at 40 km altitude. Or did he? This study was inspired by the observation that, since both sound velocity and the terminal velocity of an object vary with altitude, it is unclear whether the object's speed actually exceeds the speed of sound. The analysis compares these altitude dependent functions using a realistic non-linear frictional force and a simple but realistic model of atmospheric profiles.

Ocean Swell Modeling
The movement of a submerged object caused by ocean swell waves is a well known phenomenon, especially to those with experience SCUBA diving. While models of ocean swell power spectra are readily available, the need arose to utilize these frequency domain representations to generate realizations in the time domain. This study presents a method of generating a time series of ocean swell based on the modulation of a sine wave using a Markov-process-based random time series. Oceanography meets AM radio.

Sales Predictions
A buyer needs to accurately predict the percent of stock left at 8 weeks based on sales from the previous 6 weeks. Simple extrapolation of a least-squares line doesn't work in this case because the shrinking amount of inventory reduces the amount available for sale. An exponential model, reflecting this connection between sales and inventory, does the trick. An example of an All Experts question.
