http://ir.mksu.ac.ke/handle/123456780/685 Fri, 03 Apr 2026 17:02:59 GMT 2026-04-03T17:02:59Z http://ir.mksu.ac.ke/handle/123456780/4853 Book of proceedings of the 1st Machakos University Annual International Conference Machakos University Cognizant of the challenges and opportunities presented by the United Nations adoption of the Seventeen Sustainable Development Goals and the Government of Kenya’s Big Four Agenda: Manufacturing, Food and Nutrition security, Health and Housing, the conference further cascades the theme of the conference into five sub- themes: 1) Agriculture, Food Security, and Agribusiness for Community Transformation 2) Transformative Development through Language, Culture and Communication Technology 3) Innovative Approaches to Education and Training for Sustainable Development 4) Business and Innovative Approaches for Small and Medium Enterprise Development 5) Science, Technology, Engineering, Mathematics and Innovation for Industrial Transformation These sub-themes were crafted to embrace main drivers of sustainable development goals, namely: sharing knowledge through education; effective communication through technology; human explorations and imaginations through Science and Mathematics, sustainable, long-term growth and job creation through Small and Medium Enterprises and food for all through Agriculture and Food Security. All the sub-themes in the conference embrace innovation domains, as key driver in fast tracking economic growth based on knowledge. Innovation then must be treated as business critical in all sectors, for increased prosperity. Tue, 17 Apr 2018 00:00:00 GMT http://ir.mksu.ac.ke/handle/123456780/4853 2018-04-17T00:00:00Z http://ir.mksu.ac.ke/handle/123456780/774 Effects of Vehicles Lane-Change Manoeuvres on Traffic Breakdown and Congestion in Highways Ndungu, W.K.; Kimathi, M.M.; Theuri, D.K. Traffic breakdown is the main cause of vehicle traffic congestion in our multi-lane roads due to highway bottlenecks such as lane-drops, on and off-ramps. In this study the three phase traffic flow theory of Kerner [1] is outlined and the nature of traffic breakdown at highway bottlenecks explained. A multi-lane macroscopic traffic flow model of Aw-Rascle type is derived from kinetic traffic flow model of Klar and Wegener [2], which expresses the lane change term explicitly. For simulation of this traffic congestion, we consider a highway with three traffic lanes that has a stationary bottleneck (on-ramp). The model equations for each lane are solved numerically using finite volume method (Godunov scheme), whereby the Euler's method was used for the source term. The results of simulation near and within the bottleneck is presented in form of graphs and space-time plots. These results indicate that vehicle lane-change manoeuvres lead to heavy traffic breakdown and congestion on the right lanes compared to the left lane adjacent to the bottleneck. This is due to the merging of vehicles from on-ramp prompting the following vehicle moving in the left lane of the highway to either slow down upon reaching the disturbance region or change to the right lanes before the vehicle reaches the merging zone. Keywords: Traffic breakdown, Traffic congestion, Bottlenecks, Godunov scheme, Merging zone, Lane-change manoeuvre. Sun, 01 Apr 2018 00:00:00 GMT http://ir.mksu.ac.ke/handle/123456780/774 2018-04-01T00:00:00Z http://ir.mksu.ac.ke/handle/123456780/773 Exponentiated Generalized Geometric Burr Iii Distribution Nasiru, Suleman; Mwita, Peter N.; Ngesa, Oscar Statistical distributions play a major role in parametric statistical modeling and inference. However, most of the existing classical distributions do not provide reasonable parametric fits to data sets. Thus, the need to develop generalized versions of these classical distributions has become an issue of interest to many researchers in the field of distribution theory. This study proposes a new generalization of the Burr III distribution called the exponentiated generalized geometric Burr III distribution. Various statistical properties of the distribution such as the quantile function, moment, moment generating function, incomplete moment, mean residual life, entropy, reliability, stochastic orders and order statistics were derived. The method of maximum likelihood estimation was employed to estimate the parameters of the distribution and simulation studies were performed to investigate the properties of the estimators for the parameters of the distribution. The simulation results revealed that the estimators for the parameters were stable as the sample size increases. Application of the distribution was demonstrated using real data set to showits usefulness. Keywords: Burr III, geometric, quantile function, stochastic orders, order statistics, entropy. Sun, 01 Apr 2018 00:00:00 GMT http://ir.mksu.ac.ke/handle/123456780/773 2018-04-01T00:00:00Z http://ir.mksu.ac.ke/handle/123456780/772 Consistency of the Model Order Change-Point Estimator for GARCH Models Irungu, Irene W.; Mwita, Peter N.; Waititu, Antony G. GARCH models have been commonly used to capture volatility dynamics in financial time series. A key assumption utilized is that the series is stationary as this allows for model identifiability. This however violates the volatility clustering property exhibited by financial returns series. Existing methods attribute this phenomenon to parameter change. However, the assumption of fixed model order is too restrictive for long time series. This paper proposes a change-point estimator based on Manhattan distance.The estimator is applicable to GARCH model order change-point detection. Procedures are based on the sample autocorrelation function of squared series. The asymptotic consistency of the estimator is proven theoretically. Keywords:Autocorrelation Function, Change-Point, Consistency, Garch, Manhattan Distance, Model Order Sun, 01 Apr 2018 00:00:00 GMT http://ir.mksu.ac.ke/handle/123456780/772 2018-04-01T00:00:00Z