https://repository.maseno.ac.ke/handle/123456789/1329 2026-05-15T12:34:34Z https://repository.maseno.ac.ke/handle/123456789/5621 A comparative analysis of bornhuetter ferguson and basic chain ladder model in motor insurance: a case study of CIC insurance NYANUMBA Walter Motanya Claim reserving for motor insurance business is critically important.This has led to a slight mystery in motor insurance on how to go about claim reserving for which claims has not yet come in and there are still some figment of the future. One major critical problem in motor insurance has always been on how to calculate appropriate incurred but not reported claim reserve (IBNR) based on the data that is available on the claims that has occurred. Identifying the most appropriate model to use in modeling and estimating Incurred but not reported (IBNR) claim reserve in motor insurance has made claim reserving more intricate coupled with risks of de lay and underwriting process. This study aimed at comparing the analysis of IBNR in motor insurance using Bornhuetter Ferguson and Basic Chain Ladder model and determining the most appropriate model to use in claim reserving estimation in motor insurance so as to avoid and prevent com panies from going into financial insolvency. The objectives of this study were; to estimate and compare outstanding motor insurance claim liabil ity in each development year,evaluating and comparing the total claims for each particular accident year as well as to estimate and compare the next year’s motor insurance outstanding liability. This was achieved by applying the model in calculating outstanding reserves of motor insurance which was then determined by summing up all individual outstanding lia bility in each development year. The statistical tool used was MS. Excel. The estimates obtained from Bornhuetter Ferguson and Basic chain ladder model was then examined to determine the one that best fit the data at hand for any significant difference. This research recommended the use of basic chain ladder model since the claim development pattern was stable and there was a large amount of settled claim amount.However, both Ba sic Chain Ladder and B-F model should be applied cautiously, respecting their circumstance under usage by combining them with their subjective assessment of actuaries based on their expertise and experience. 2022-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5332 Mathematical modeling of flood wave: a case study of Budalang’i flood plain basin in Busia county, Kenya MIHESO, Stephen Musindayi Flooding is a worldwide problem with more adverse effects in developing countries. In Kenya, severe flooding is experienced on the lower tributaries of Lake Victoria, mainly Budalang’i area. This is indicated in the historical floods of 2003, 2007, 2017 and 2019, leading to mass displacement of people and property destruction. This has attracted attention of researchers worldwide and application of different measures to curb flood in the study regions. Mathematical modeling of flood wave has however not been adopted in Budalang’i flood plain. Therefore this study formulated, analyzed and simulated the 2D flood wave model with incorporation of a sink to the Budalangi flood plain. Formulation was applied on existing Navier Stokes equations with the addition of a sink term on continuity equation. Analy sis of the shallow water model entailed transforming the equations using Jacobian transformation and assessing the nature of flow using Froude number. For simula tions of the 2D shallow water model, the study adopted a finite difference scheme to make approximations which solved the system of equations and displayed in the figures . It is realized that in the formulation of the 2D shallow equations, appro priate model for Budalang’i flood plain is easily derived from the 3D Navier Stokes equations under flood plain assumptions and addition of a sink term is necessary for modelling in the flood plain. Assessment of the properties reveals that super critical flows are dominant. Addition of a sink term ensures steady state velocity thus reducing higher frequency and turbulence as well as over bank flows while incorporating coriolis term has significant effect on the turbulence. The study concludes that addition of a sink term to the 2D shallow water model will enable control of the floods in the area of study. The findings will aide disaster manage ment stakeholder to come up with a more reliable flood prevention technique and new knowledge on how source terms can help reduce flood risk. Masters Theses 2022-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5165 Modeling Mechanistic-Empirical Road Design: The Case for Kenyan Roads NYAKITI, Samson Agia Regular revision of road design manuals is a recommended practice in pavement management, and Kenya has recently completed a review of hers. The outcome of the process is an enhanced but empirical manual with rigid models. The reviewers (BCEOM egis, a geotechnical consul tancy) however strongly recommended the use of interactive mathemati cal models of a mechanistic-empirical (ME) nature in road design for the country in future, since ME models more accurately predict pavement performance than the rigid ones currently in empirical manuals. Using ME models in road design in Kenya now is a challenge since the climatic models in ME design require inputs of hourly intervals, yet most weather stations keep only daily interval records. This study investigated the pos sibility of adapting the existing ME mathematical models for use in road design in Kenya. We achieved this by rigorously analyzing the differ ential equations and other equations contained in the ME mathematical models. Simulating hourly weather data from daily data was applied for some weather elements, while adaptation of the governing equations in the models to take inputs of daily intervals was done for the others. Secondary climatic data obtained from the Kenya Meteorological Depart ment and theWeatherbase websites were used as inputs into the models. The study established that with suitable adaptation, the existing climatic data can be used as inputs into the models with little loss in the relia bility of their predictions, hence Kenya can successfully embrace the ME pavement approach. The findings of this study could serve as an initial step towards the realization of the reviewers' recommendations on use of ME mathematical models over empirical manuals. 2011-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5162 Calculations for Mutations of Quivers with Potential' WAMBUA, Victoria Mwia From the work of Derksen, Weyman and Zelevinsky in [4], we get the definition for mutation of a quiver with potential. Stern in [l~l describes . some families of quivers corresponding to quivers with potential that can be mutated indefinitely. In this work, we use two of these ialliilies as our basic examples ofstudy and find their appropriate potentials. Because the potentials get larger and larger with the mutations, weuse two notations; first, a brief one and the second one providing useful information about the individual potentials. The results of this study offer explicit examples of quivers with potential which can be studied further 2011-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5153 Mathematical Model of the Roan Antelopes, Ruma Park OCHIENG', Daniel Achola Roan antelopes that were once abundant in the country in the 1880s have been reduced to a remnant population of less than fifty individuals in the last estimate,November 2009. Oksendal and Lungu developed population growth model in a crowded environment by introducing randomness in their differential equation via additional noise term. Magin and Kock in their roan antelope recovery plan in the Ruma National Park considered poaching as a major factor affecting population growth of roans which saw a slight population growth before experiencing stagnation since the year 2003 to date. The Kenya Wildlife Service (KWS) has since taken neces sary measures to curb poaching. This reduced the risk of poaching as a major factor that accelerated roans' population decay. Lambwe valley is believed to have uranium deposits that could affect fertility. Inbreeding in small populations is known to have substantial effects on population growth rate. We have therefore incorporated in our model genetic defect that was not incorporated by Magin and Kock. This was made possi ble by making appropriate adjustments to Vortex Version 9.99 which is a computerized program for the simulation of the extinction processes. We noted that there is a high correlation between inbreeding and popu lation growth in small populations. It is hoped that this study will help The Kenya Wildlife Service (KWS) in the management of their complex ecosystem. 2011-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5137 Evaluation of Adequacy and Level of Utilization of Sanitation Facilities in Primary Schools in Manga Sub County, Nyamira, County, Kenya WANYONYI, Joyce Nandako Good sanitation and hygiene practices promote the wellbeing of children in schools. According to WHO(World Health Organization), 88% of all diarrheal related illnesses result from poor sanitation and hygiene practices as well as unsafe water. In addition, UN Secretary General and Millennium Projects have highlighted the need to address sanitation facilities in schools. This is not just limited to inclusion of 80% of school children educated on hygiene but also that all schools are equipped with adequate sanitation facilities. This study sought to find out the adequacy and utilization of sanitation facilities among school going children in Manga Sub County, Nyarnira County. To achieve the set objective 10 schools were selected to participate in the study. A chi-square test was used to find out whether there was association between awareness of pupils on consequences of poor sanitation and utilization of the sanitation facil ities. All the 10 schools used pit latrines for their disposal of fecal matter while 8 schools had hand washing facilities in place. Latrines were found to be inadequate in 8schools having below minimum standard of latrine to pupil ratio of 1:25 for girls and 1:30 for boys set by the Ministry of Health in collaboration with Ministry of Education. Chi square test showed a significant association. APvalue of 0.04 was achieved in a test comparing awareness/knowledge and utilization of available sanitation facilities. Thus the need for schools to enforce utilization of the available sanitation facilities, put in more effort to build additional facilities as well as equip the hand washing facilities by ensuring continuous. availability of water all geared towards promoting utilization. 2016-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5130 A Stochastic and Deterministic Predator- G Prey Population Model for Sustainable Harvesting: A Case of Nile Perch Lates Niloticus and Nile tilapia Oreochromis Niloticus OMONDI, Jael Olwande Predation by Nile perch is one of the main causes of fish stock depletion in Lake Victoria. Uncontrolled human exploitation (overfishing) of the stock leads to loss of fish biodiversity in Lake Victoria. Increasing the harvesting rates of mature Nile perch can lead to stable stationary states. However, increasing the predation rates of Nile perch can lead to unstable ecosystem. Predation, coupled with uncontrolled harvesting have been a major ecological force in shaping the present day fishing communities on Lake Victoria, in particular and other lakes at large. The challenges currently facing Lake Victoria is how to sustain the Nile perch, Nile tilapia and how to conserve and restore threatened fish species. In this study, we will apply the Lotka Volterra competition model (1925) for predator and prey population. The objective of this study is therefore to develop a predator- prey model for Nile perch and Nile tilapia based on standard Lotka- Volterra predator prey model. The methodology involves formulation of a system of ordinary differential equations where prey ratio is incorporated. in this model. The finding in this study could be used to predict and explain the effect of predation by Nile perch on tilapia so that control of Nile perch can result in conservation and restoration of threatened fish species. The model is also a contribution of knowledge in mathematical modeling. 2012-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5110 On Joint Essential Numerical Ranges CYPRIAN, Omukhwaya Sakwa The concept of numerical range on a Hilbert space was first introduced by O. Toeplitz in 1918 for matrices. This notion was independently ex tended by G. Lumer and F. Bauer in the sixties on finite dimensional Banach spaces. J. G. Stampfli introduced the maximal numerical range, proved its convexity and used it to derive an identity for the norm of derivation in 1970. In 1972, J. G. Stampfli and J. P. Williams defined and studied the essential numerical range of an operator. In our work, we looked at the joint essential numerical ranges. In particular, this study has shown that the properties of numerical ranges such as com pactness, nonemptiness and convexity do hold for the joint essential nu merical range. The study has also shown that the closure of the joint numerical range of an operator is star-shaped with elements in the joint essential numerical range of the operator as star centers. Further, we have shown that the joint essential spectrum is contained in the joint essen tial numerical range by looking at the boundary of the joint spectrum. Convexity, nonemptiness and compactness of the joint essential numerical range were shown by first proving the equivalent definitions of the joint essential numerical range. Basing on the convexity of the joint essential numerical range, other results were obtained. The results of this study are helpful in the development of the research on numerical ranges and may also be applied by mathematicians in solving several problems in operator theory. 2013-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5103 Perceptions Versus Realities on Climate Change in the Sugarcane Growing areas of Chemelil and Muhoroni OPANY, Daniel Okoth Perception on climate change is a prerequisite for adaptation. A number of studies have been conducted to investigate perceptions on climate change. However, they rarely incorporate analysis of climatic data to corroborate the findings. This study is a two- pronged attempt to determineperceptions on climate change and to establish if they match the reality. Face to face interviewshave been conducted on individuals at household levels in 15villages in Chemelil and Muhoroni Sugarcane growing area of Kisumu County involving 405 adult residents to elicit perceptions.Climatic data consisting mainly of daily rainfall data for 23 years from Muhoroni SugarCompany's central weather station has been analyzed to provide evidence on reality on the same. Using InStat, a statistical package specially designed for analysis of climatic data.and another, GenStat; descriptive statistics, inferential analysis of climatic events for trends and Markovchain modelling of rainfall data have been utilized Chi-square tests for independence, t- . test for equality of two means and regression analysis have been employed. The feelings of the respondents tended to be influenced more by their perceived demands for rainfall. The overall perception among gender irrespective of level of education was that there is climate change. However, exploration and analysis of long term daily rainfall data do not reveal statistical evidenceof the same. Involving statistical analysis of climatic data would validate and reinforce evidence based on perception and guide in more informed policy formulation and decision makingon climate change related issues. 2013-01-01T00:00:00Z https://repository.maseno.ac.ke/handle/123456789/5100 The Statistical Modeling of Retail Business Processes in Nyakach District OMOLLO, Thadius Oriema Multivariate statistical analysis of retail business processes was done in this study. Multiple predictor variables were included in the regression model. Meta-analysis of the correlations were also used to explore heterogeneity and to estimate central tendency and variation in the effects. It was our observation that many retail businesses started in Nyakach District either don't do well or collapse within the first few years of their operation. Reasons for this trend were numerous and unsatisfactory besides being less quantitatively statistical.It was against this background that we were inspired to statist ically model retail business processes in this region to investigate the effects of capital, business age and floor area among other factors, on business performance using regression and correlation analysis. We built models, vigorously analyzed and interpreted the same in an attempt to examine how value could be created and captured in a business unit. Wehave therefore provided a broad review of literature on business models in which we examined the business models concept through multidisciplinary and subject matter lenses. 2013-01-01T00:00:00Z