Other Statistics and Probability Commons^™

On The Transmuted Distributions; Properties And Application, Jacob D. Kretzer

Theses, Dissertations and Capstones

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 …

Random Variable Spaces: Mathematical Properties And An Extension To Programming Computable Functions, Mohammed Kurd-Misto

Computational and Data Sciences (PhD) Dissertations

This dissertation aims to extend the boundaries of Programming Computable Functions (PCF) by introducing a novel collection of categories referred to as Random Variable Spaces. Originating as a generalization of Quasi-Borel Spaces, Random Variable Spaces are rigorously defined as categories where objects are sets paired with a collection of random variables from an underlying measurable space. These spaces offer a theoretical foundation for extending PCF to natively handle stochastic elements.

The dissertation is structured into seven chapters that provide a multi-disciplinary background, from PCF and Measure Theory to Category Theory with special attention to Monads and the Giry Monad. The …

Species Discovery And Diversity In Lobocriconema (Criconematidae: Nematoda) And Related Plant-Parasitic Nematodes From North American Ecoregions, Tom Powers, Ernest C. Bernard, T. Harris, Robert Higgins, M. Olson, S. Olson, M. Lodema, Julianne N. Matczyszyn, P. Mullin, L. Sutton, K.S Powers

Department of Statistics: Faculty Publications

There are many nematode species that, following formal description, are seldom mentioned again in the scientific literature. Lobocriconema thornei and L. incrassatum are two such species, described from North American forests, respectively 37 and 49 years ago. In the course of a 3-year nematode biodiversity survey of North American ecoregions, specimens resembling Lobocriconema species appeared in soil samples from both grassland and forested sites. Using a combination of molecular and morphological analyses, together with a set of species delimitation approaches, we have expanded the known range of these species, added to the species descriptions, and discovered a related group of …

Using The R Library Rpanel For Gui-Based Simulations In Introductory Statistics Courses, Ryan M. Allison

Statistics

As a student, I noticed that the statistical package R (http://www.r-project.org) would have several benefits of its usage in the classroom. One benefit to the package is its free and open-source nature. This would be a great benefit for instructors and students alike since it would be of no cost to use, unlike other statistical packages. Due to this, students could continue using the program after their statistical courses and into their professional careers. It would be good to expose students while they are in school to a tool that professionals use in industry. R also has powerful …