Date of Award

2024

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Dr. Raid Al-Aqtash, Committee Chairperson

Second Advisor

Dr. Alfred Akinsete

Third Advisor

Dr. Laura Adkins

Abstract

The transmuted distributions first appeared in (2007) after Shaw and Buckley constructed a quadratic rank transmutation map (QRTM), G(u) = (1 + λ)u − λu2, as a transformation of a cumulative distribution function of a random variable X, to generate the transmuted-X distribution. In (2017), Jayakumar & Babu defined the T -transmuted-X family of distributions by incorporating a transmuted-X into a transformer-transformed class of distributions (Aljarrah et al., 2014). This thesis surveys the main properties of the transmuted-X distribution, such as density shapes, moments, and entropy. Detailed attention will be given to existing members of the transmuted-X family of distributions, such as the transmuted-Weibull (Aryal & Tsokos, 2011) and the transmuted-exponentiated Gumbel (Deka et al., 2017). A new member of the T -transmuted-X, namely the Gumbel-Transmuted-Weibull, is presented and statistical properties of the new distribution are investigated. Real data from literature is used in application of the proposed distribution, in comparison with other existing distributions in literature.

Subject(s)

Mathematics.

Statistics.

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