http://hdl.handle.net/123456789/954 2026-04-14T23:27:46Z 2026-04-14T23:27:46Z Manu, Jones Asante http://hdl.handle.net/123456789/12219 2025-06-09T11:46:51Z 2023-12-01T00:00:00Z

Quartic Rank Transmutation of Gamma–Type Distributions: Characteristics and Estimation Manu, Jones Asante Rank transmutation maps have emerged as one of the adopted methods for proposing new probability distributions. This study used the quartic rank transmutation to introduce three new probability distributions: the Quartic Transmuted Exponential Distribution, Quartic Transmuted Lindley Distribution, and Quartic Transmuted Rayleigh Distribution. The construction of these distributions involves meticulously examining mathematical concepts, encompassing probability density functions, survival functions, moments, entropies, and order statistics. Visual aids, including cumulative distribution functions, probability density functions, and hazard rate functions, enhance the comprehension of distribution characteristics. A comprehensive simulation study underscores a consistent trend: a reduction in bias for maximum likelihood estimation and refinement in standard errors with increasing sample size. The practical applicability of these newly proposed distributions was demonstrated using real-world datasets. The quartic transmuted exponential distribution was effectively employed to model the lifetime of 50 devices, referencing data from Aarset’s study in 1987. Similarly, the quartic transmuted Lindley distribution was adeptly applied to remission times (measured in months) of 128 bladder cancer patients. Finally, the quartic transmuted Rayleigh distribution was successfully utilized to analyze a dataset comprising 72 instances of exceedance from the Wheaton River flood data near Carcoss in Yukon Territory, Canada. Evaluation criteria such as log-likelihood, AIC, AICc, and BIC affirm the superior flexibility and performance of the proposed distributions. This research significantly contributes to distribution theory, offering innovative methods to enhance distribution adaptability in diverse applications. xi, 171p:, ill.

2023-12-01T00:00:00Z Chataa, Paul http://hdl.handle.net/123456789/12200 2025-06-05T13:41:45Z 2024-07-01T00:00:00Z

Mathematical Model of Immune Response to Hepatitis B Virus and Liver Cancer Co-Existence Dynamics in the Presence of Treatment Chataa, Paul The principal method for modeling the spread of infectious diseases generally involves the application of ordinary differential equations. Studies have demonstrated that an effective strategy for refining certain mathematical models is the integration of fractional-order differential equations. To gain a more profound understanding of the interactions between the hepatitis B virus (HBV), liver cancer, and immune system cells, a mathematical model that combined both ordinary and fractional differential equations was investigated. This model was closely aligned with experimental data on viral DNA load. The work concentrated on four qualitative scenarios: the innate immune response, adaptive immune response, cytokine response, and the coexistence of infection dynamics. Unlike earlier models, liver cells were classified into distinct stages of infection. For populations of non-pathogenic macrophages in the presence and absence of malignant cells, the study calculated the invasion probability for transmission dynamics, represented by the control reproduction number, Rc. The iterated two-step Adams-Bashforth method was employed for numerical simulations using the ABC fractional derivative in the Caputo sense, while the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC) techniques were utilized for parameter sensitivity analysis. The work identified the key transmission mechanism of viral load and proposed an optimal therapeutic method for viral treatment. Model parameters were estimated using nonlinear least squares fitting of longitudinal data (serum HBV DNA viral load) from existing literature. Finally, the study compared the classical-order model system with the ABC fractional differential equations model system to determine which offered superior performance. Both methods were evaluated using simulation results of the state variables, revealing that the fractional model provides more detailed results than the classical model. xvi, 226p:, ill.

2024-07-01T00:00:00Z Bandoh, Bernard Bonsu http://hdl.handle.net/123456789/12197 2025-06-05T13:18:54Z 2024-08-01T00:00:00Z

The Conjecture of Group Structure: The Relationship Between The Alpha Invariant and Nilpotency in Finite Groups Bandoh, Bernard Bonsu In this research work, we acknowledge and explore the relation between the alpha value and non-nilpotent groups, leading to the proof of a conjecture put forward in research by Cayley (2021). We demonstrate that if 𝐺 is non-nilpotent and 𝛼(𝐺) = 􀬷 􀬸 then 𝐺 ≅ 𝐷􀬶􀬸 × 𝐶􀬶􀳙 , with a nontrivial centre, where 𝑛 ∈ {0, 1}. Furthermore, we conclude that the conjecture holds for 𝐺 ≅ 𝐷􀬶􀬸 × 𝐶􀬶􀳙 as well. We again prove, using both computational and theoretical techniques, that a subgroup which is nontrivial in 𝐺 exists with both normal and characteristic properties. We finally prove a theorem related to the count involving subgroups, cyclic in nature, of finite groups 𝐺 where |𝐶(𝐺)| = |𝐺| − 6. Thus, we demonstrate that if 𝐺 is one of the groups 𝐷􀬶􀬸, 𝐶􀬵􀬶, 𝐶􀬽, 𝐶􀬵􀬴, 𝐷􀬵􀬼, or 𝐷􀬶􀬴, then |𝐶(𝐺)| = |𝐺| − 6. xii, 109p:, ill.

2024-08-01T00:00:00Z GYASI-AGYEI, KWAME ASARE http://hdl.handle.net/123456789/11538 2025-01-23T15:16:20Z 2024-03-01T00:00:00Z

Discriminant Canonical Correlation Analysis Of Time-Dependent Multivariate Data Structure GYASI-AGYEI, KWAME ASARE Canonical Correlation Analysis (CCA), which is a widely used covariance analysis method is a technique that is not fundamentally designed for multivariate multiple time-dependent data (MMTDD) structure that could be suitably partitioned on two subsets of response and predictor variables. This means that for such data problems, the conventional CCA would not yield practical results. The literature also shows scanty work in this area. This study therefore designs and implements grouping scheme discriminant canonical correlation analysis (GSDCCA) for handling this problem so that the time effect is adequately captured in the computation of the correlation coefficient between the two sets of variables. It first identifies key matrices underlying the concert and presents the design in both theory and illustration. Using data on six weather conditions in Ghana spanning the period 2000 to 2021, the demonstrations show that correlation coefficient between heating and cooling sets of weather conditions varies at different time points, and that the overall correlations are quite higher than that obtained from data assumed to be time-independent. The procedure is therefore recommended as an innovative approach for handling MMTDD. xvii,200p:, ill.

2024-03-01T00:00:00Z