May 23, 2023
Graduating this semester from Shawnee State University, Scott Ferrell (Hometown: Chesapeake, Ohio) presented his own research at this year’s Celebration of Scholarship conference on campus. A Mathematical Sciences major with a concentration in Actuarial Science, Ferrell’s research “Maximum Likelihood Estimation on Time Scales” was presented during the Poster Session and received the Outstanding Poster Presentation Award from the conference committee.
“My poster summarizes one of the research projects I worked on at a research experience for undergraduates this past summer,” he said. “In building a probability model of a population, it is of interest to find good estimators of what the parameters of the population's probability distribution might be. In our research, my research group applied the process of maximum likelihood estimation to time scales probability distributions, which are neither fully continuous nor fully discrete.”
In his presentation, Ferrell made sure to go into detail regarding his research and its practical application in everyday circumstances.
“For example, imagine you own a business that is open 9:00 a.m. – 5:00 p.m. on Monday through Friday and you order something for your business,” he said. “You want to use the data of your past orders to estimate when you can expect to receive the next order. However, the times that you can receive the package are not continuous since you cannot receive the package when the business is closed, and the times are not discrete either since you are interested in exactly what time during the day you receive the package. Instead of being classically discrete or continuous, the times at which you can receive the package are a set of separate continuous intervals. Therefore, classically discrete or continuous probability distributions cannot be used to model the receipt time of packages. However, time scales probability distributions generalize the classical distributions so that they can be applied to more general time scales such as when your business is open.”
In his original research group, him and his team were able to find maximum likelihood estimators for time scales exponential and time scales uniform distributions. They found in what cases the new estimators differ from the classical estimators, and then they built simulations to compare the new and classical estimators in some of the cases that they differ. They found that their new estimators generally perform better than the classical estimators on the time scales in which they differ.
“I greatly enjoyed presenting at Celebration of Scholarship,” he said. “It is always a pleasure to be able to share my work with other people who are curious about math but maybe do not have the same background as me.”
On receiving the Outstanding Poster Presentation Award, Ferrell was extremely grateful. He believes it is an indication that he can communicate mathematics effectively and share his work and his passion with others regardless of how little background in mathematics they might have.
“I am very grateful to the professors who lead the research experience for undergraduates, the professors at SSU who helped me gain the knowledge and reasoning to perform this research, and the conference coordinators who have given me a platform to share my work,” he said.
To learn more about the annual Celebration of Scholarship conference at Shawnee State University, visit shawnee.edu/cos.