Date of Award
2025
Degree Name
Mathematics
College
College of Science
Type of Degree
M.A.
Document Type
Thesis
First Advisor
Dr. Raid Al-Aqtash
Second Advisor
Dr. Alfred Akinsete
Third Advisor
Dr. Laura Adkins
Abstract
Developing new statistical distributions and seeking higher flexibility in modeling different shapes of data remain a strong emphasis in research. The T-R{Y } framework, introduced in [3], utilizes three statistical distributions in order to generate a new distribution. Many research papers appeared in literature to develop distributions based on the T-R{Y } framework. In this thesis, a member of the T-R{Y } framework, namely the Gumbel-Weibull{Cauchy} (GWC), is introduced. Statistical properties of the GWC are studied, such as the quantile function, the hazard function, transformations, Shannon entropy, the mean deviation from the mean, the mean deviation from the median, and moments. The method of maximum likelihood is used for parameter estimation. Multiple real data sets are utilized to illustrate the usefulness of using the method of maximum likelihood in parameter estimation, and the fits are compared to existing distributions in the literature.
Subject(s)
Mathematics.
Statistics.
Mathematical models.
Statistical distributions and models with applications.
Recommended Citation
Pippin, Jennifer D., "On the Gumbel-Weibull{Cauchy} distribution" (2025). Theses, Dissertations and Capstones. 1907.
https://mds.marshall.edu/etd/1907
