The work in this thesis is based on research carried out in the Department of Mathematical Sciences at Durham University. No part of this thesis has been submitted elsewhere for any degree or qualification.

Nonparametric predictive inference for comparison of two diagnostic tests.', Communications in statistics-theory and methods. .

No abstract

In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution. Some structural properties of the newly suggested model are obtained. Different types of entropies are proposed under the TCP-ITL distribution. Under the complete and hybrid censored data, the maximum likelihood (ML), maximum product of spacing (MPSP), and Bayesian estimate approaches are explored. A simulation study is developed to test the proposed distribution’s restricted sample attributes. In the majority of cases, the numerical data revealed that the Bayesian estimates provided more accurate outcomes than the equivalent alternative estimates. The adaptability of the proposed approach is proven using examples from dependability, medicine, and engineering. A real-world data set is utilized to demonstrate the potential of the TCP-ITL distribution in comparison to other well-known distributions. The results of the model selection revealed that the proposed distribution is the best choice for the data sets under consideration.

In clinical applications, it is important to compare and study the ability of diagnostic tests to discriminate between individuals with and without the disease. In this paper, comparison of two diagnostic tests is presented and discussed using nonparametric predictive inference (NPI). We compare the two tests by considering the total numbers of correct diagnoses for specific numbers of future healthy individuals and future patients. This NPI approach for comparison of diagnostic tests is also generalized by the use of weighted sums for the healthy and patients groups, reflecting possibly different importance of correct diagnoses. Examples are provided to illustrate the new method.