Mathematics and Statistics
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Item Modelling Fluid Flow in Zone 1 of an Open Horseshoe Channel with Lateral Inflow Channels(Journal of Advances in Mathematics and Computer Science, 2024-05-24) Jomba Jason; Mark Okongo; Jacob Kirimi; Jimrise OnyangoFor many years, flooding has been a significant issue, especially after heavy rainfall. Engineers have constructed channels to direct water into rivers, lakes, and oceans, aiming to mitigate flooding. The challenge lies in designing drainage ditches, irrigation canals, and navigation channels that maximize hydraulic efficiency for water transport and electricity generation. Most studies have focused on rectangular, parabolic, trapezoidal, and circular open channels, leaving a knowledge gap in the study of horseshoe-shaped channels with lateral inflows. This research aims to model a uniform flow in Zone 1 with a horseshoe-shaped cross- section and lateral inflows. The study aimed to determine how variations in the angle of lateral inflowchannels and the increase in lateral inflows in Zone 1 affect the main channel flow velocity. Governing equations were derived by applying conservation equations to the physical conditions of the flow. These equations were solved using the finite difference approximation method due to its precision, stability, and convergence. The results, presented graphically, revealed that the main channel velocity decreases as the number of lateral inflow channels increases. Ultimately, the main channel velocity decreases as the angles of the lateral inflows increase. Mitigating floods and collecting water for irrigation drive scientific, technological, and engineering progress by demanding creative remedies and infrastructure that enhance crop production and tolerance to climate changes. By enhancing food security and enabling sustainable farming practices, these developments promote economic growth and raise living standards in communities while also generating job possibilities. Water management that incorporates scientific and technological advancements allows society to more effectively utilize natural resources, which in turn promotes greater socioeconomic empowerment.Item Modeling Open Channel Fluid Flow Past a Trapezoidal Cross-section with a Segment Base having Lateral Inflow Channel(Journal of Advances in Mathematics and Computer Science, 2024-07-11) Charles Mwaniki Nyaga; Mark Okongo; Jacob KirimiFloods in flood-stricken areas have been a major threat to the survival of lives and livelihoods in various aspects. For instance, increased pot-holes, road disconnection and tearing off as well as bridges being carried away have led to increased cases of accidents leading to loss of lives. This has led to Government over- stretching budgetary allocations to cater for maintenance and repair of roads and bridges. This study has developed a model for fluid flow past an open channel with a trapezoidal cross-section with a segment base having lateral inflow channel. The turbulent formation between the lateral inflow channel and the main channel are assumed to be negligible and hence the flow is laminar. The model equations governing the fluid flow are non-dimensionalized and solved using finite-difference method. The numerical values are simulated using Matlab software. It is found that an increase in cross-section area of the lateral channel increases the discharge in the main channel leading to an increase in flow velocity. An increase in surface roughness increases shear stress thereby recording a reduced flow velocity. The findings of this study is highly applicable in the design of drainage systems for road construction, sewer building, street drainage, dams, and airport construction in Kenya and elsewhere. Moreover, the designed efficient channels with optimal dimensions are applicable in draining water to hydro-electric power plants where large volumes of high velocity water are required to turn large turbines for electrical processes.Item Developing a Model for Open Channel Fluid Flow with a Segment Base having Lateral Inflow Channel(Journal of Advances in Mathematics and Computer Science, 2024-09-13) Charles Mwaniki Nyaga; Mark Okongo; Jacob KirimiAn open channel fluid flow is characterized by presence of a free surface. The interface between two homogeneous fluids of different densities is regarded as free surface. It is the surface of the liquid that is in contact with air. Generally, this interface is subject to zero parallel shear stress. The survival of lives and livelihoods has greatly been hampered by occurrence of floods. When there is heavy downpour, accumulation of flooded water has led to bridges being washed away, increased pot holes on the roads and this has led to increased cases of accidents leading to loss of lives. This has posed a huge financial burden to the Government in terms of budgetary allocations to import human capital for maintenance and repair of worn out roads and bridges. This study has developed a model for fluid flow past an open channel with a trapezoidal cross-section with a segment base having lateral inflow channel that has optimal dimensions for maximum discharge. The fluid particles throughout the flow do not crisscross each other and hence the entire flow is assumed to be laminar. The developed model equations are non-dimensionalized, discretized and solved using finite-difference method and numerical values are simulated using Matlab Mathematical software. The findings are discussed, analyzed and presented graphically. It is reported that an increase in length of the lateral channel leads to decrease in flow velocity of the main channel. An angle of inclination of the lateral channel at a range of 300 to 450 exhibit higher values of flow velocity in the main channel compared to other angles. However, maximum velocity at the main channel is attained at an inclination angle of 300. At this angle, there is minimum shear stress hence less resistance to the flow profile. The results of this study is highly applicable in the design of drainage systems for road construction, sewer building, street drainage, airport construction and dams for electric power plants in Kenya and elsewhere.Item Correspondence of Fixed-Point Theorem in � �𝟐, 𝑻𝟑 − 𝑺𝑷𝑨𝑪�(Asian Research Journal of Mathematics, 2024-08-19) Amos Koros; Musundi Sammy Wabomba; Mark OkongoFixed-point theory (FPT) has lot of applications not only in the field of mathematics but also in various other disciplines. Fixed Point Theorem presents that if 𝑇: 𝑋 → 𝑋 is a contraction mapping on a complete metric space (𝑋, 𝑑) then there exists a unique fixed point in 𝑋. FPT is also essential in game theory, in this case Brower Fixed Point has an application in game theory specifically in non-cooperative games and existence of Equilibrium. In particular, a game is a set of actions done by the participants defined by a set of rules. This is commonly described using mathematical concepts, which offers a concrete model to describe a variety of situations. On the other hand, the separation axioms 𝑇𝑖, 𝑖 = 0,1,2,3,4 are vital properties that describes the topological spaces 𝑇0 , 𝑇1 , 𝑇2, 𝑇3 and 𝑇4 . It is noted that a 𝑇3 − 𝑠𝑝𝑎𝑐𝑒 is a generalized version of 𝑇2-space and since various results on application of fixed point theory in game theory on an arbitrary locally convex � �2 − space has been established, in this study we sort to extend this concept to the general 𝑇3 − 𝑠𝑝𝑎𝑐𝑒. The utilization of a symmetric property of Hausdorff space established that if two continuous commutative mappings are defined on a 𝑇3 − 𝑠𝑝𝑎𝑐𝑒, then the two maps achieves unique fixed points.Item Mathematical Model of the Impact of Home-Based Care on Contagious Respiratory Illness Under Optimal Conditions(JAMBURA JOURNAL OF BIOMATHEMATICS, 2024-12-30) Henry Milimo Wanjala; Mark O. Okongo; Jimrise O. OchwachMathematical models are vital for understanding real-world phenomena without direct experimentation, particularly in epidemics, as they predict and analyze the effectiveness of various mitigation strategies. Given the rapid transmission of infectious respiratory diseases, public health measures aim to curb spread while managing impacts. This study assesses rapid contact tracing and testing, focusing on isolating confirmed cases through home-based care or traditional methods, on coronavirus transmission within a community.A deterministic mathematical model using ordinary differential equations segments the population into seven compartments: susceptible, exposed, asymptomatic, symptomatic, home-based care, hospitalized, and recovered. The basic reproduction number is determined via the next generation matrix. Local stability of the disease-free equilibrium is analyzed using the trace-determinant method, while global stability is confirmed with the Lyapunov-Krasovskii approach. A Python-based numerical simulation on NumPy and PyPlot uses parameters calibrated to previous studies and estimated for this research. Simulations indicate home-based care delays peak infection days and reduces peak population, providing time to bolster healthcare facilities. Optimal control methods, including media awareness, reduce susceptibility and encourage asymptomatic individuals to choose home-based care. Using Pontryagin's Maximum Principle, the study identifies optimal strategies, highlighting that media awareness effectively lowers susceptibility and optimal control directs asymptomatics to home-based care, reducing strain on healthcare facilities. In conclusion, home-based care is effective for managing mild symptomatic and asymptomatic cases, alleviating pressure on healthcare resources and prioritizing severe cases. Combining home-based care with other non-pharmaceutical strategies is recommended for maximum effectiveness.Item On The Norm of Elementary Operator of Length Two In Tensor Product Of C*-Algebras(|International Journal of Mathematics|, 2024-12-14) Peter Guchu MuiruriConsiderable research has been done on Norm property of different examples of Elementary operators with significant findings. From available literature not much have been done in determining the norm of elementary operator in tensor product of C*-algebras. The norms of Basic elementary operator, Jordan elementary operator and finite length elementary operator in tensor product of C*-algebras have been determined and results obtained. The main focus of this work is to investigate the norm of the elementary operator of length two in the tensor product of C*-algebras and to expand on our previous discussion on the elementary operator in tensor product of C*-algebras. To reach the goals, methods such as finite rank operator, tensor products of C*-algebras, and other well-known results were applied.Item Statistical Modelling of Staff Survival Time in Service at Chuka University(Asian Journal of Probability and Statistics, 2025) Waka Olivia; Dennis K. Muriithi; Mark Okong’o aStaff attrition is identified as a major challenge affecting the education sector globally and in Kenya. The main objective of this study is to develop a statistical model of staff survival time in service at Chuka University. The study investigated seven covariates (Gender, age group, Marital Status, Terms of employment, staff Category, staff Highest Qualifications and Job group) on the outcome variable which is staff survival time in Service at Chuka University. In this research, survival analysis methods that were used are the Kaplan Meier and log rank test, the Cox-proportional hazard model and the Accelerated Failure Time models (Weibull AFT Model). The cox proportional regression model was employed to study the effect of the covariates on the survival time of the staff at Chuka University. To compare the survival rate of different groups of staff, the study employed the use of Kaplan Meier Estimator. To test if a difference exists in survival time between two or more independent groups, this study applied log-rank test. The results on the Univariate Cox PH Model showed that the covariates, gender, age group, terms of employment, staff category, highest qualification and Job group were statistically significant at 5% level of significance except for the Marital status which was insignificant associated with the survival time of staff at Chuka University. The study was able to predict the probability of survival of staff using the covariates. The findings from the study showed that the male staff have high survival probability compared to their female counterparts: the younger employees between the age of 18-25 stay in service for fewer years compared to those between the age of 26-35 and 36-50. Further results indicated that, The Weibull AFT model give the best model fit with more precise estimates that had small standard errors compared to the Cox Proportional Hazard Model. These findings will be beneficial for the policy makers to review the policies related to staff retention at different Universities in Kenya and more especially to the Chuka University, Human Resource Management to make informed decisions and implement strategies to improve staff retention and more effective recruitment strategies. These policies include Professional Development Programs: Universities may offer ongoing training and development opportunities, such as workshops, certifications, and seminars, to help staff improve their skills and advance their careers. Also Universities can offer competitive salaries, performance- based bonuses, and comprehensive benefits packages (health insurance, retirement plans, tuition waivers) to retain staff.Item Application of Principal Component Analysis and Hierarchical Regression Model on Kenya Macroeconomic Indicators.(EJ-MATH, European Journal of Mathematics & Statisctics., 2022) Mbaluka, M. K.; Njoroge, G. G.; Muriithi, D. K.The aim of this paper was to apply Principal Component Analysis (PCA) and hierarchical regression model on Kenyan Macroeconomic variables. The study adopted a mixed research design (descriptive and correlational research designs). The 18 macroeconomic variables data were extracted from Kenya National Bureau of Statistics and World Bank for the period 1970 to 2019. The R software was utilized to conduct all the data analysis. Principal Component Analysis was used to reduce the dimensionality of the data, where the original data set matrix was reduced to Eigenvectors and Eigenvalues. A hierarchical regression model was fitted on the extracted components, and R2 was used to determine whether the components were a good fit for predicting economic growth. The results from the study showed that the first component explained 73.605 % of the overall Variance and was highly correlated with 15 original variables. Additionally, the second principal component described approximately 10.03% of the total Variance, while the two variables had a higher positive loading into it. About 6.22% of the overall variance was explained by the third component, which was highly correlated with only one of the original variables. The first, second, and third models had F statistics of 2385.689, 1208.99, and 920.737, respectively, and each with a p-value of 0.0001<5% was hence implying that the models were significant. The third model had the lowest mean square error of 17.296 hence described as the best predictive model. Since component 1 had the highest Variance explained, and model 1 had a lower p-value than other models, Principal component 1 was more reliable in explaining economic growth. Therefore, it was concluded that the macroeconomic variables associated with the monetary economy, the trade and openness of the economy with government activities, the consumption factor of the economy, and the investment factor of the economy predict economic growth in Kenya. The study recommends that PCA should be utilized when dealing with more than 15 variables, and hierarchical regression model building technique be used to determine the partial variance change among the independent variables in regression modeling.Item Primitivity Action of the Cartesian Product of an Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples(London Journals Press, 2022) Maraka, M. K.; Musundi, S. W.; Nyaga, L. N.In this paper, we investigate the primitivity action properties of the cartesian product of an alternating group 𝐴 (𝑛≥5) 𝑛 acting on a cartesian product of ordered sets of triples using the definition primitivity and blocks. When 𝑛≥5, the cartesian product of the alternating group, 𝐴 × 𝐴 × 𝐴 𝑛 𝑛 𝑛 , acts imprimitively on a cartesian product of ordered sets of triples, , [3] [3] [3]. Mathematics Subject Classification: 20B05; 20B15; 20B20Item Singular Spectrum Analysis: An Application to Kenya’s Industrial Inputs Price Index(EJ-MATH, European Journal of Mathematics and Statistics., 2022) Emmanuel, K. K.; Wagala, A.; Muriithi, D. K.Time series modeling and forecasting techniques serve as gauging tools to understand the time-related properties of a given time series and its future course. Most financial and economic time series data do not meet the restrictive assumptions of normality, linearity, and stationarity of the observed data, limiting the application of classical models without data transformation. As non-parametric methods, Singular Spectrum Analysis (SSA) is data- adaptive; hence do not necessarily consider these restrictive assumptions as in classical methods. The current study employed a longitudinal research design to evaluate how SSA fist Kenya’s monthly industrial inputs price index from January 1992 to April 2022. Since 2018, reducing the costs of industrial inputs has been one of Kenya’s manufacturing agendas to level the playing field and foster Kenya’s manufacturing sector. It was expected that Kenya’s Manufacturing Value Added hit a tune of 22% by 2022. The study results showed that the SSA (L = 12, r =7) (MAPE = 0.707%) provides more reliable forecasts. The 24-period forecasts showed that the industrial inputs price index remains high above the index in 2017 before the post-industrial agenda targeting a reduction in the cost of industrial inputs. Thus, the industrial input prices should be reduced to a sustainable level.Item Vector Error Correction Model: Prediction of Bi-Directional Causality between Gross Domestic Product and Wage Growth in Kenya(European Journal of Mathematics and Statistics, 2022) Njoroge, M. S.; Njoroge, G. G.; Wagala, A.Economic growth and wage growth are very prominent macroeconomic variables in all countries in the World. These two variables are the main signposts signaling the current trends in an economy. To determine the recent behavior of the economy, the government must study and analyze these major variables. The increase in aggregate production in the Kenyan economy has been deteriorating due to the steady rise in the wage bill, especially since the year 2012, in conjunction with the devolved government. An increase in wage rate motivates workers and, in turn, increases the production capacity of a country hence economic growth. An increase in recurrent expenditure implies that the development expenditure will be condensed, which will alter the growth of the economy. The primary goal of this research was to fit vector error correction model on gross domestic product and wage growth data so as to identify the bidirectional causality effects between the two variables. VEC model is superior since it distinguishes between long run and short run relationship among underlying variables in a large sample size. The linear Granger causality test was used to evaluate the causal relationship between the system's variables; hence a causal research design was adopted in this study. This research employed secondary data, which was analyzed using Eviews and STATA statistical software. Data on these target variables was acquired from the World Bank and Central Bank of Kenya. Lastly, this study used yearly time series data for the period 1979 to 2019. It was found that wage growth and GDP granger causes each other and also have a long run relationship since their respective p values were less than 5% significance level. VECM1 (effects of wage growth on GDP) had AIC of -0.2953, RMSE of 1.0039 while the R-squared was 0.7241. Subsequently, effects of GDP on wage growth (VECM2) was found to have an R-squared of 0.7452, AIC of -8.2270 and RMSE of 0.08363. Based on the foregoing findings, it was determined that GDP has more influence on wage growth both in the short and long run. This study thus recommends that the government should keep inflation under control, increase development expenditure to finance projects and fostering a favorable business environment for Small and Medium-sized Enterprises (SMEs) to upsurge total output (productivity) which will in turn, lead to a rise in wage growth, thus a high standard of living for the millions of unemployed Kenyans. Finally, the findings of the current study are expected to be of significance to academicians and also provide appropriate policy options that will help in harmonizing the wage rates, thus managing recurrent expenditure in Kenya.Item Demystifying Mathematics: handling learning difficulties in Mathematics among low achievers in Kenyan schools(Journal of Language, Technology & Entrepreneurship in Africa, 2022) Njoroge, Gladys GakeniaMathematics is a compulsory subject in both primary and secondary schools in Kenya. However, learners’ poor performance in the subject in Kenya national examinations year in year out remains a serious concern for teachers of Mathematics, parents, curriculum developers, and the general public. This is particularly worrying because of the importance attached to the subject in national development hence the need to find out what could be affecting learning of Mathematics in Kenyan schools. The research on which this paper is based sought to examine the factors that influence performance in Mathematics in Kenyan schools; identify the characteristics of Mathematics learning disabilities; determine how the learners with such learning disabilities can be assessed and identified and interventions for these difficulties implemented. A case study was undertaken on class six learners in a primary school in Nairobi County. The tools used for the research were: classroom observations and an Individualized Education Program (IEP) developed by the teachers with the help of the researcher. This paper therefore highlights the findings from the research, discusses the implications of the findings and suggests the way forward as far as teaching, learning and assessment of Mathematics in Kenyan schools is concerned. Perhaps with the application of the right interventions, poor performance in Mathematics in the national examinations in Kenya will be a thing of the past.Item On Analytical Approach to Semi-Open/Semi-Closed Sets(International Journal of Discrete Mathematics., 2017-03-03) Musundi, Sammy Wabomba; Kinyili, Musyoka; Ohuru, Priscah MoraaThe concept of open and closed sets has been extensively discussed on both metric and topological spaces. Various properties of these sets have been proved under the underlying spaces. However, scanty literature is available about semi-open /semi- closed sets on these spaces. For instance, little effort has been made in introducing these sets as clopen sets in topological spaces but no literature exists of the same under metric spaces. In this paper, with reference to the already existing definitions and properties of open and closed sets in metric spaces as well as in topological spaces we shall present definitions of semi-open/ semiclosed sets and furthermore prove basic properties of these sets on metrics spaces. The results of the study will provide a deeper understanding as well as extension knowledge for the concept of open and closed sets to their somewhat counter-intuitive terms of semi- open /semi-closed.Item Equilibrium Equity Premium in a Semi Martingale Market When Jump Amplitudes Follow a Binomial Distribution(Scientific Research Publishing Inc., 2018-08-20) Mukupa, George M.; Offen, Elias R.This paper studies equilibrium equity premium in a semi martingale market when jump amplitudes follow a binomial distribution. We take n to be the number of times. An investor is trading in this market with p being the probability that there is a shift in the price at the trading time t. We find significant variations in the equilibrium equity premium for the martingale and semi martingale markets in terms of wealth value, volatility and other parameters under study. In this market, the equilibrium equity premium remains constant regardless of volatility and wealth value.Item Derivation of Fixed-Point Theorem Using Expansive Mapping Approach(Asian Research Journal of Mathematics, 2023-06-07) Koech Vincent a , Musundi W. Sammy a* and Kinyanjui JeremiahApplication of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if is a contraction mapping on a complete metric space then there exists a unique fixed point in . A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of , the Sierpinski triangle also with contraction constant of . On the other hand, a mapping on such that is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.Item Primitivity Action of the Cartesian Product of an Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples(London Journal Press, 2022) Maraka, Moses K., Musundi, Sammy W., Nyaga, Lewis N.In this paper, we investigate the primitivity action properties of the cartesian product of an alternating group 𝐴 (𝑛≥5) 𝑛 acting on a cartesian product of ordered sets of triples using the definition primitivity and blocks. When 𝑛≥5, the cartesian product of the alternating group, 𝐴 × 𝐴 × 𝐴 𝑛 𝑛 𝑛 , acts imprimitively on a cartesian product of ordered sets of triples, [3] [3] [3].Item Modeling and Forecasting Kenyan GDP Using Autoregressive Integrated Moving Average (ARIMA) Models(Science Publishing Group, 2016-04-13) Musundi, Sammy Wabomba; M’mukiira, Peter Mutwiri; Mungai, FredrickThe Gross Domestic Product (GDP) is the market value of all goods and services produced within the borders of a nation in a year. In this paper, Kenya’s annual GDP data obtained from the Kenya National Bureau of statistics for the years 1960 to 2012 was studied. Gretl and SPSS 21 statistical softwares were used to build a class of ARIMA (autoregressive integrated moving average) models following the Box-Jenkins method to model the GDP. ARIMA (2, 2, 2) time series model was established as the best for modeling the Kenyan GDP according to the recognition rules and stationary test of time series under the AIC criterion. The results of an in-sample forecast showed that the relative and predicted values were within the range of 5%, and the forecasting effect of this model was relatively adequate and efficient in modeling the annual returns of the Kenyan GDP. Finally, we used the fitted ARIMA model to forecast the GDP of Kenya for the next five years.Item A NOTE ON QUASI-SIMILARITY OF OPERATORS IN HILBERT SPACES(International Journal of Mathematical Archive, 2015-07-23) SAMMY W. MUSUNDI; ISAIAH N.SITATI; BERNARD M. NZIMBI; KIKETE W. DENNISIn this paper we introduce the notion of Quasi-similarity of bounded linear operators in Hilbert Spaces. We do so by defining a quasi- affinity from one Hilbert Space H to K. Some results on quasi- affinities are also discussed. It has already been shown that on a finite dimensional Hilbert Space, quasi similarity is an equivalence relation that is; it is reflexive, symmetric and also transitive. Using the definition of commutants of two operators, we give an alternative result to show that quasi similarity is an equivalence relation on an infinite dimensional Hilbert Space. Finally, we establish the relationship between quasi similarity and almost similarity equivalence relations in Hilbert Spaces using hermitian and normal operators.Item The Banach Numerical Range for Finite Linear Operators(Modern Scientific Press Company, 2020-02-14) M. Ohuru, Priscah; W. Musundi, SammyThe numerical range has been a subject of interest to many researchers and scholars in the recent past. Based on the research outputs, many results have been obtained. Besides, several generalizations of the classical numerical range have also been made. The recent developments have focused on the theory of operators on Hilbert spaces. The determination of the numerical ranges of linear and nonlinear operators have been given in both the Hilbert and Banach spaces. In addition, results of these numerical ranges have been extended to the case of two operators in both spaces. It is important to note that more generalizations have been made in Hilbert spaces as compared to those that have been made in the Banach spaces. The Banach space has two major numerical ranges which are: the spatial and algebraic numerical ranges. This research focuses on determining the numerical range for a finite number of linear operators in the Banach space based on the classical definition. Properties which hold for the classical numerical range have been shown to hold for the Banach space numerical range. The property of convexity has been established using the Toeplitz-Hausdorff theorem under the condition that the Banach space is smooth. Furthermore, the numerical radius and the spectrum of these operators have also been determined.Item PLS Generalized Linear Regression and Kernel Multilogit Algorithm (KMA) for Microarray Data Classification Problem(Revista Colombiana de Estadística - Applied Statistics, 2020) Wagala, Adolphus; González-Farías, Graciela; Ramos, RogelioThis study involves the implentation of the extensions of the partial least squares generalized linear regression (PLSGLR) by combining it with logistic regression and linear discriminant analysis, to get a partial least squares generalized linear regression-logistic regression model (PLSGLR-log), and a partial least squares generalized linear regression-linear discriminant analysis model (PLSGLRDA). A comparative study of the obtained classifiers with the classical methodologies like the k-nearest neighbours (KNN), linear discriminant analysis (LDA), partial least squares discriminant analysis (PLSDA), ridge partial least squares (RPLS), and support vector machines(SVM) is then carried out. Furthermore, a new methodology known as kernel multilogit algorithm (KMA) is also implemented and its performance compared with those of the other classifiers. The KMA emerged as the best classifier based on the lowest classification error rates compared to the others when applied to the types of data are considered; the unpreprocessed and preprocessed.