Date of Award

2025

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Dr. Tom Cuchta

Second Advisor

Dr. Alfred Akinsete

Third Advisor

Dr. Raid Al-Aqtash

Abstract

We shall investigate Gompertz dynamic equations within the context of time scales calculus, by exploring the mathematical foundations and applications of the Gompertz model, which is commonly used to describe growth phenomena in various fields such as biology and economics. This research seeks to analyze the Gompertz cumulative distribution functions (CDF) and probability density functions (PDF) across different time scales, including the real numbers R and integer multiples hN. Probability techniques will be used to derive the CDF and PDF associated with the Gompertz dynamic equations, and we will examine how varying the time scale impacts the characteristics of these distributions. Through graphical representations, we intend to facilitate a comparative analysis that elucidates the relationship between time dynamics and growth patterns. This work aims to contribute to the field of applied statistics by providing insights into the integration of timescale calculus with Gompertz modeling, thereby establishing a foundation for further research into dynamic systems and their statistical properties.

Subject(s)

Mathematics.

Mathematical models.

Measure theory.

Probabilities.

Mathematical statistics.

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