#### Presentation Title

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.