Maximum Likelihood Estimation on Time Scales
University
Shawnee State University
Major
Mathematical Science with Actuarial Concentration
Presentation Types
Poster Presentation
Keywords:
Maximum Likelihood Estimation, Time Scales, Probability
Abstract
When developing a probabilistic model for independently sampled data, good estimates for the parameters of the potential models are critical. One method for finding good estimates is the maximum likelihood estimator (MLE), which uses calculus techniques to maximize the probability of obtaining the observed data for varying values of the underlying parameter. Time scales, closed subsets of the real line, have recently arisen and provide a means to understand classical probability distributions as special cases of more general distributions on time scales. So, while the classical exponential distribution is valued on , and the geometric distribution on , both can be seen as special cases of a more general “time scales exponential” distribution. We find general formulas for the MLEs for the parameters of the time scale exponential and time scales uniform distributions and see how their MLEs compare both algebraically and computationally to the MLEs of the classical distributions.
Human Subjects
no
IRB Approval
yes
Faculty Mentor Name
David DeSario
Faculty Mentor Title
Associate Professor
Faculty Mentor Academic Department
Mathematical Sciences
Recommended Citation
Ferrell, Scott, "Maximum Likelihood Estimation on Time Scales" (2023). Celebration of Scholarship. 1.
https://digitalcommons.shawnee.edu/cos/2023/Day4/1
Maximum Likelihood Estimation on Time Scales
When developing a probabilistic model for independently sampled data, good estimates for the parameters of the potential models are critical. One method for finding good estimates is the maximum likelihood estimator (MLE), which uses calculus techniques to maximize the probability of obtaining the observed data for varying values of the underlying parameter. Time scales, closed subsets of the real line, have recently arisen and provide a means to understand classical probability distributions as special cases of more general distributions on time scales. So, while the classical exponential distribution is valued on , and the geometric distribution on , both can be seen as special cases of a more general “time scales exponential” distribution. We find general formulas for the MLEs for the parameters of the time scale exponential and time scales uniform distributions and see how their MLEs compare both algebraically and computationally to the MLEs of the classical distributions.