RP-Department of Statistics and Actuarial Science

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A Hybrid Approach for Predicting Probability of Default in Peer-to-Peer (P2P) Lending Platforms Using Mixture-of-Experts Neural Network
(2024-05) Makokha, Christopher Watitwa; Kube, Ananda; Ngesa, Oscar
Peer-to-peer (P2P) lending offers an alternative way to access credit. Unlike established lending institutions with proven credit risk management practices, P2P platforms rely on numerous independent variables to evaluate loan applicants’ creditworthiness. This study aims to estimate default probabilities using a mixture-of-experts neural network in P2P lending. The approach involves coupling unsupervised clustering to capture essential data properties with a classification algorithm based on the mixture-of-experts structure. This classic design enhances model capacity without significant computational overhead. The model was tested using P2P data from Lending Club, comparing it to other methods like Logistic Regression, AdaBoost, Gradient Boosting, Decision Tree, Support Vector Machine, and Random Forest. The hybrid model demonstrated superior performance, with a Mean Squared Error reduction of at least 25%.
A Lightweight Convolutional Neural Network with Hierarchical Multi-Scale Feature Fusion for Image Classification
(Scientific Research Publishing, 2024-02) Dembele, Adama; Mwangi, Ronald Waweru; Kube, Ananda Omutokoh
Convolutional neural networks (CNNs) are widely used in image classification tasks, but their increasing model size and computation make them challenging to implement on embedded systems with constrained hardware resources. To address this issue, the MobileNetV1 network was developed, which employs depthwise convolution to reduce network complexity. MobileNetV1 employs a stride of 2 in several convolutional layers to decrease the spatial resolution of feature maps, thereby lowering computational costs. However, this stride setting can lead to a loss of spatial information, particularly affecting the detection and representation of smaller objects or finer details in images. To maintain the trade-off between complexity and model performance, a lightweight convolutional neural network with hierarchical multi-scale feature fusion based on the MobileNetV1 network is proposed. The network consists of two main subnetworks. The first subnetwork uses a depthwise dilated separable convolution (DDSC) layer to learn imaging features with fewer parameters, which results in a lightweight and computationally inexpensive network. Furthermore, depthwise dilated convolution in DDSC layer effectively expands the field of view of filters, allowing them to incorporate a larger context. The second subnetwork is a hierarchical multi-scale feature fusion (HMFF) module that uses parallel multi-resolution branches architecture to process the input feature map in order to extract the multi-scale feature information of the input image. Experimental results on the CIFAR-10, Malaria, and KvasirV1 datasets demonstrate that the proposed method is efficient, reducing the network parameters and computational cost by 65.02% and 39.78%, respectively, while maintaining the network performance compared to the MobileNetV1 baseline.
A Jump Diffusion Model with Fast Mean-Reverting Stochastic Volatility for Pricing Vulnerable Options
(Hindawi, 2023) Nthiwa, Joy K.; Kube, Ananda O.; Omari, Cyprian O.
Te Black–Scholes–Merton option pricing model is a classical approach that assumes that the underlying asset prices follow a normal distribution with constant volatility. However, this assumption is often violated in real-world fnancial markets, resulting in mispricing and inaccurate hedging strategies for options. Such discrepancies may result into fnancial losses for investors and other related market inefciencies. To address this issue, this study proposes a jump difusion model with fast mean-reverting stochastic volatility to capture the impact of market price jumps on vulnerable options. Te performance of the proposed model was compared under three diferent error distributions: normal, Student-t, and skewed Student-t, and under diferent market scenarios that consist of bullish, bearish, and neutral markets. In a simulation study, the results show that our model under skewed Student-t distribution performs better in pricing vulnerable options than the rest under diferent market scenarios. Our proposed model was ftted to S&P 500 Index by maximum likelihood estimation for the mean and volatility processes and Gillespie algorithm for the jump process. Te best model was selected based on AIC and BIC. Samples of the simulated values were compared with the S&P 500 values and MSE computed at various sample sizes. Values of MSE at diferent sample sizes indicate signifcant decrease to actual MSE values demonstrating that it provides the best ft for modeling vulnerable options.
Product Quality Influencing Production Reshoring Decision among Manufacturing Multinational Corporations in Kenya
(2018) Gatundu, James; Oloko, Margaret; Letting, Nicholas; Kahiri, James
This study sought to identify the strategic drivers influencing reshoring decision among manufacturing multinational corporations in Kenya and was guided by the following research objectives; finding out extent to which production cost, product quality, operational flexibility, reduced time to market and hidden cost influenced production reshoring decision. It also considered the moderating effect of market condition on reshoring decision. The study adopted cross sectional design and census method targeting 96 manufacturing multinational corporations drawn from membership of Kenya Association of Manufacturers with a response rate of 88.9%. Descriptive analysis, factor analysis, multicollinearity test, ANOVA test and logistic regression test were carried out for each variable. Statistical Package for Social Sciences Version 24 was used as the tool for data analysis. The study found out that product quality have positive influence on production reshoring decision. The combined effect of all independent variables and the moderating variable reflected a positive effect of 78.9% on the dependent variable. The study model was also found to be the optimal model for the study. The major recommendations from the study was to improve capacity to service unique customer orders. Finally, the government should strengthen intellectual property laws and enhance their enforcement to reduce incidences of counterfeit products. This would improve overall Kenyan manufacturing entities competitiveness and reduced unfair competition from counterfeit products.
A Statistical Application of Regression Analysis to Investigate and Determine the Factors that Influence the Uptake of Family Planning in Meru County, Kenya
(SSRN Blog, 2022) Mpuria, Thomas Bundi; Kahiri, James
Family planning is one of the mitigation factors adopted by the Kenyan Government in achieving its strategic development goals through reducing maternal and child mortality, preventing unwanted pregnancies, preventing STDs, promoting education, and women's economic empowerment. Despite the many advantages of family planning, its use and adoption in Kenya are still low. Unwanted pregnancies, premature deliveries, illegal abortions, and maternal mortality have all resulted from a low uptake of family planning. The low application of family planning methods has been associated with low awareness of the existence of family planning services, lack of information about various forms of family planning services, and negative attitude toward some family planning methods due to lack of counseling/sensitization to mothers on their side effects, complex in assessing the family planning services by some rural women, religious beliefs and fear of not being able to bear children again. South Imenti is a Sub County in Meru County associated with low uptake of family planning services despite providing free family planning services in all government clinics. The goal of this study was to employ the regression method to examine factors that impact the usage of family planning methods in the South Imenti sub-county. The target population was 3390 women between the ages of 15 and 49. A total of 385 mothers were chosen using simple random sampling from the target population for this survey. The study used descriptive and binary logistic regression methods of analysis. The explanatory variables included education level, age, marital status, Number of children born, Religion, Occupation, household income, and frequency of listening to media. In conclusion, the application of the binary logistic regression model on the data collected showed that age, marital status, level of education, number of children mothers have, and frequency of mothers following media were potential explanatory variables that significantly affected the use of family planning methods. The education level of women of childbearing age 15-49 years had the highest significant effect on the usage of family planning.
Hierarchical Penalized Mixed Model
(Scientific Research Publishing, 2019) Ndung’u, A. W.; Mwalili, S.; Odongo, L.
Penalized spline has been a popular method for estimating an unknown function in the non-parametric regression due to their use of low-rank spline bases, which make computations tractable. However its performance is poor when estimating functions that are rapidly varying in some regions and are smooth in other regions. This is contributed by the use of a global smoothing parameter that provides a constant amount of smoothing across the function. In order to make this spline spatially adaptive we have introduced hierarchical penalized splines which are obtained by modelling the global smoothing parameter as another spline.
Significance of Coriolis F Significance of Coriolis Force on E ce on Eyring-P yring-Powell Flow Ov owell Flow Over A Rotating Non-uniform Surface
(Digital Commons @PVAMU, 2021) Oke, Abayomi Samuel; Mutuku, Winifred Nduku
Coriolis force plays significant roles in natural phenomena such as atmospheric dynamics, weather patterns, etc. Meanwhile, to circumvent the unreliability of Newtonian law for flows involving varying speed, Eyring-Powell fluid equations are used in computational fluid dynamics. This paper unravels the significance of Coriolis force on Eyring-Powell fluid over the rotating upper horizontal surface of a paraboloid of revolution. Relevant body forces are included in the Navier-Stokes equations to model the flow of non-Newtonian Eyring-Powell fluid under the influence of Coriolis force. Using similarity transformation, the governing equations are nondimensionalized, thereby transforming the nonlinear partial differential equations to a system of boundary value nonlinear ordinary differential equations. The shooting technique is adopted to convert the boundary value problem to an initial value problem, which is in turn solved using the Runge-Kutta-Gill Scheme. At low Coriolis force, temperature profiles increase as Eyring-Powell parameter increases, whereas at high Coriolis force, temperature profiles decrease with increasing Eyring-Powell parameter.
Newtonian Heating on MHD Stagnation-Point Flow over a Flat Plate
(FUW Trends in Science & Technology Journal, 2021) Oyem, Anselm O.; Mutuku, Winifred; Edogbanya, Helen O.; Oke, Samuel; Garbas, Babangida B.
A study on incompressible, steady magnetohydrodynamic (MHD) stagnation point flow of an electrically conducting fluid over a flat plate with variable thermal diffusivity and Newtonian heating has been considered. The governing partial differential equations were transformed using suitable similarity variables to couple nonlinear differential equations. The transformed equations are solved using the Runge-Kutta fourth order scheme with the shooting technique method. The effects of the various dimensionless flow parameters are presented in tables and graphs in terms of velocity and temperature profiles. Numerical computations for skin friction coefficient and Nusselt number are done. It was observed that thermal radiation parameter decreases the rate of heat transfer on the surface but increases in skin-friction coefficient while, increase in the viscosity and thermal diffusivity variation parameter increases both the skin-friction coefficient and rate of heat transfer. The results are in conformity with existing results
Modeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking Dynamics
(Journal of Advances in Mathematics and Computer Science, 2021) Nyamai, Amos Mwendwa; Mutuku, Winifred N.
Aims: 1. Develop and analyze a mathematical model of the effect of inpatient rehabilitation of tobacco smokers on tobacco smoking using Kenya as a case study. 2. Perform stability analysis on the smoking free equilibrium point and endemic equilibrium point of the model. 3. Use numerical simulation to investigate the impact of inpatient rehabilitation of tobacco smokers on smoking. Place and Duration of Study: Department of Mathematics and Actuarial Science, School of Pure and Applied Sciences (SPAS), Kenyatta University, Kenya, between May 2019 and September 2020. Tobacco smoking is a serious burden in Kenya and the world at large. Smoking harms nearly every organ of the body and affects the overall health of a person. Despite the overwhelming facts about the consequences of tobacco smoking, it remains a bad wont which is socially accepted and widely spread. In this research we numerically analyze the dynamics of smoking incorporating the impact of inpatient rehabilitation to curb the smoking habit. We first present a three-compartment model incorporating inpatient rehabilitation, then develop the system of ordinary differential equations governing the smoking dynamics. The basic reproduction number is determined using next generation matrix method. The model equilibria were computed and the stability analysis carried out. The results of stability analysis indicate that the disease-free equilibrium (DFE) is both locally and globally asymptotically stable for RS < 1 while the endemic equilibrium is both locally and globally asymptotically stable for RS > 1. Numerical simulations of model carried out with the help of MATLAB shows that, when rehabilitation is implemented effectively, it helps in minimization of smoking in the community
Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement
(Hindawi Publisher, 2021) Kithinji, Martin M.; Mwita, Peter N.; Kube, Ananda O.
In this paper, we propose an extreme conditional quantile estimator. Derivation of the estimator is based on extreme quantile autoregression. A noncrossing restriction is added during estimation to avert possible quantile crossing. Consistency of the estimator is derived, and simulation results to support its validity are also presented. Using Average Root Mean Squared Error (ARMSE), we compare the performance of our estimator with the performances of two existing extreme conditional quantile estimators. Backtest results of the one-day-ahead conditional Value at Risk forecasts are also given.
Analysis of Ethylene Glycol (EG)-based ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) Hybrid Nanofluids for Optimal Car Radiator Coolant
(Journal of Engineering Research and Reports, 2020) Okello, John A.; Mutuku, W. N.; Oyem, A. O.
Coolants are vital in any automotive since they manage the heat in the internal combustion of the engines by preventing corrosion in the cooling system as well as assist in eradicating the engine’s waste heat. This paper examines three different types of ethylene glycol-based hybrid nanofluids ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) to establish their cooling capabilities for industrial cooling applications. The vertical flow of these hybrid nanofluids combination through a semi-infinite convectively heated flat plate mimicking the flow of coolant in car radiator is modeled. The governing non-linear partial differential equations of fluid flow are transformed into a system of coupled non-linear ordinary differential equations using a suitable similarity transformation variables and the numerical solution executed using the shooting technique together with the fourth-order Runge-Kutta-Fehlberg integration scheme. The numerical simulation is executed using MATLAB and results are displayed graphically. The effects of pertinent parameters on velocity, temperature, skin friction, and local Nusselt number are investigated. From the study (Cu-Al2O3 hybrid nanocoolant leads to a rapid decrease in temperature at the boundary layer.
A study of simple and multiple relations between mathematics attitude, academic motivation and intelligence quotient with mathematics achievement
(Elsevier, 2013) Ogeto, Abuta
Purpose of current study was to investigate simple and multiple relations between mathematics' attitude, academic motivation and intelligence quotient with mathematics achievement. The Statistical population involved the entire Ardabil province' high schools students in 2008 (N = 33982). From these, 1670 students are selected as sample by using Cochran's formula and multiple cluster sampling. For gathering data, the following instrument is used. Raven IQ test (=0.86), Hermense Academic Achievement Test (=0.83), Moenikia mathematics attitude questionnaire (=0.79), and students' mathematics score in final exam. Correlation method was the research method. For data analysis, Pearson coefficient correlation and multiple regression in enter model were used. The Results showed that all of the variables correlate with together significantly. Mathematics' attitude, academic motivation, and intelligence quotient were predicator of mathematics achievement statistically significant. Keywords: Mathematics attitude; academic motivation; intelligence quotient; mathematics achievement.
Model-Assisted Estimation of Population Mean in Two-Stage Cluster Sampling
(University of the Punjab, 2017) Bii, Nelson Kiprono; Onyango, Ouma Christopher
Estimation of finite population parameters has been an area of concern to statisticians for decades. This paper presents an estimation of the population mean under a model-assisted approach. Dorfman (1992), Breidt and Opsomer (2000) and Ouma et al (2010) carried out the estimation of finite population total on the assumption that the sample size is large and the sampling distribution is approximately normal. Unlike their researches, this paper considered a case when the sample size is small under a model-assisted approach. A model-assisted regression model was considered in a case where the cluster sizes are known only for the sampled clusters in order to predict the unobserved part of the population mean. Under mild assumptions, the proposed estimator is asymptotically unbiased and its conditional error variance tends to zero. Simulation studies show that model assisted estimation performs better than model based estimation of a finite population mean in a case where the sample size is small.
A new regression type estimator with two auxiliary variables for single-phase sampling
(Scientific Research Publishing, 2014) Tum, Everline Chemutai; Kung’u, John; Odongo, Leo
In this paper, we have proposed an estimator of finite population mean using a new regression type estimator with two auxiliary variables for single-phase sampling and investigated its finite sample properties. An empirical study has been carried out to compare the performance of the proposed estimator with the existing estimators that utilize auxiliary variables for finite population mean. It has been found that the new regression type estimator with two auxiliary variables for to be more efficient than mean per unit, ratio and product estimator and exponential ratio and exponential product estimators and exponential ratio-product estimator

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