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This dissertation develops a first-order multivariate Poisson integer-valued autoregressive (MPINAR(1)) model to improve disease outbreak detection in public health surveillance systems. The MPINAR(1) model is proposed as a computationally tractable alternative to the general multivariate...

This dissertation develops a negative binomial integer-valued generalized autoregressive conditional heteroscedastic model of order p, q (negative binomial INGARCH(p, q)) for overdispersed count time series data with potential extreme values. The model is formulated such that its conditional...

This study aims to obtain a lower bound on the eigenvalue of the smallest modulus in a general weighted regular Sturm-Liouville problem with mixed boundary conditions. The problem is expressed as -u′′(x) + q(x)u(x) = λr(x)u(x) over the interval [a,b] with u′(a) = u(b) = 0. In 1988 Mingarelli [31]...

This study aimed to determine the maximum likelihood (ML) estimates for the Gamma and Exponential distributions under conditions of left-truncated and right-censored data, employing the Expectation-Maximisation (EM) algorithm. Additionally, it sought to compare the performance of the EM algorithm...

In this dissertation we obtain quasi-deformations of the special linear Lie algebra of degree 2 over a eld F, abbreviated sl2(F). We take F to be a eld of characteristic zero. Our approach involves obtaining and deforming a linear operator representation of sl2(F) using-twisted derivations (with...

In this thesis we study some of the properties of homogeneous spaces. We are more interested in homogeneous spaces which are also manifolds. We have shown that homogeneous spaces are basically quotient spaces. Working with quotient spaces, we pushed to symplectic quotient, the...

In this thesis, we recall three types of convexities in metric spaces, namely; Menger convexity, Takahashi convexity andM-convexity. We then generalise these convexities to the framework of T0-quasi-metric spaces. Since the concept of convexities heavily relies on the concept of betweenness, a...

The concept of hyperconvexity in metric spaces was introduced by Aronszajn and Panichpakdi in 1956. This concept was then generalised to the framework of quasi-metric spaces by John Isbell in 1964, which he called Isbell convexity. In 2019, Yi git and Efe generalised this concept of...

A commutatively ordered Banach algebra (COBA) is a complex unital Banach algebra A containing a subset C, called an algebra c-cone, such that C contains the unit of A and is closed under addition, positive scalar multiplication and multiplication by commuting positive elements. If the...

This study establishes the asymptotic consistency of the James-Stein shrinkage estimator (JSSE) ˆ!⇤ n of some parameter ✓, which is obtained by shrinking a maximum likelihood estimator (MLE) ˆ✓n. Our shrinking strategy involves creating a subspace to shrink to by partitioning the parameter space...