Statistics and Actuarial Science

A principal component analysis of the key determinant factors of teenage pregnancy: a case of secondary school Girls in Ndhiwa sub-county, Kenya

2025-11-13T08:16:49Z

A principal component analysis of the key determinant factors of teenage pregnancy: a case of secondary school Girls in Ndhiwa sub-county, Kenya OKONGO, Ochieng Wilberforce Teenage pregnancies occurrence and incidences vary significantly across different regions. High rates or low rates of adolescent pregnancies are often attributed to varying degrees of influence from several determinant factors.This study sought to identify key determinant factors of teenage pregnancy among secondary school girls in Ndhiwa sub-county using principal component analysis (PCA).Teenage pregnancy remain a significant challenge in many communities including Ndhiwa Sub-County where its prevalence threaten the education and future prospects of adolescent girls. Despite various intervention, the rate still remains high suggesting that deeper data driven insight required to identify key factors influencing it occurrence in the region. PCA is a statistical method that simplifies multivariate data by reducing variables while retaining essential information.In this study PCA was used to explore highly significant determinant factors of teen pregnancy among secondary school females in Ndhiwa Sub-county, specifically determining among 10 determinant factors namely, age of the teenager, peer pressure, family factor (poverty), lack of communication between daughter and parent, electronic media use, lack of contraceptive awareness, lack of knowledge on fertile period, lack of sex education, drugs and substance abuse, and early sex debut (pre-marital sex) which would significantly contribute to teenage pregnancy. The study was conducted in selected girls' secondary schools in Ndhiwa subcounty. This institutional-based cross-sectional study involved 379 participants selected through random and cluster sampling from a target population size of 7128 female students. Data was collected using a structured questionnaire with responses measured on a 5-point Likert scale. Statistical analyses including correlation analysis, descriptive statistics, and PCA were performed using SPSS version 25. The study found a 14.2% prevalence of teenage pregnancy among secondary school girls in Ndhiwa sub-county. Notably, peer pressure showed a strong positive correlation with premarital sex, suggesting predictive potential. PCA identified four principal components peer pressure, early sexual debut, substance abuse, and lack of communication between daughter and parent as crucial, explaining 51.13% of the determinant factors' variability. These findings can guide stakeholders and policymakers in developing targeted interventions to reduce teenage pregnancy rates among school-going girls. Master's Thesis

A multivariate analysis of variance of feed intake, Milk, and manure yields of crossbreed dairy Cows Across different diets0225

2025-11-12T07:28:55Z

A multivariate analysis of variance of feed intake, Milk, and manure yields of crossbreed dairy Cows Across different diets0225 ODEDE, patrick ayako Dairy farming plays a crucial role in Kenya’s agricultural sector, contributing 6% to 8% of the country’s Gross Domestic Product. Enhancing the efficiency of commonly used diets in this sector is of utmost importance. This study aimed to investigate the overall effect of six treatments on three response variables in dairy cows, namely, feed intake, milk yield and manure yield. Improving the efficiency of dairy farming diets is essential for the growth and sustainability of the industry in Kenya. However it is necessary to identify the effects of the treatments on key variables such as feed intake, milk yield and manure yield to make informed decisions and optimize dairy production. Understanding the effects of different treatments on feed intake, milk yield, and manure yield in dairy cows can lead to improved practices and increased efficiency in the dairy sector. This knowledge can contribute to better decision making regarding diet formulation and resource allocation, ultimately benefiting farmers, dairy industry, and overall economy. Randomized Complete Block Design (RCBD) was employed to evaluate the effect of six treatments, namely Napier grass (A), Napier grass and Lucerne Hay (B), Napier grass silage (C), Napier grass silage and Lucerne Hay (D), Rhodes grass (E), and Rhodes grass and Lucerne Hay (F) on six crossbreed cows. Treatments were randomly allocated within each block and the experiment was conducted at the Dairy Research Institute (DRI) of the Kenya Agricultural and Livestock Research Organisation (KALRO) in Naivasha. This study employed a Multivariate Analysis of Variance (MANOVA) using Pillai’s Trace test statistics to determine the overall treatment effects on the three response variables. The analysis revealed a statistically significant multivariate effect [Pillai′sTrace = 1.2137, F = 3.3971, P<0.05] among the six treatments on feed intake, milk yield and manure yield with effect size Partial Eta Squared (η2 p=0.40). This indicated a moderate effect, where 40% of the variance in the overall dependent variables was attributable to the treatment factor, suggesting that the treatments had a moderate influence on the overall dependent variables under study. To further examine the significant difference within the treatments, a Linear Discriminant Analysis (LDA), a multivariate Post-Hoc test was conducted. The results identified two groups of treatments: (A, B,C, and D) and (E,F). The study provides valuable insights into the effect of different treatments on feed intake, milk yield, and manure yield in dairy cows. The findings can guide farmers in making informed decisions regarding diet formulation and optimizing dairy production. Master's Thesis

Fitting and validation of logistic regression models For long-acting reversible contraception and Unplanned pregnancy among adolescents and young Women in rural Kenya.

2025-11-11T12:37:52Z

Fitting and validation of logistic regression models For long-acting reversible contraception and Unplanned pregnancy among adolescents and young Women in rural Kenya. OKOTH, Henry Nyumba In rural Kenya, adolescent girls and young women face significant challenges in accessing and utilizing Long-Acting Reversible Contraceptives (LARC) and continue to experience a high prevalence of unplanned pregnancies. Previous studies have primarily focused on women of all reproductive ages, with limited attention given to the unique circumstances of adolescents and young women living in rural regions. This study aimed to identify socio-demographic and predictive factors influencing LARC use and unplanned pregnancies among adolescent girls and young women in rural Kenya, utilizing logistic regression analysis. Additionally, it validated the logistic regression models employed in identifying these determinants. The study used nationally representative secondary data from the Performance Monitoring for Action (PMA) survey, which employed a multi-stage stratified cluster design. The study population included adolescent girls and young women from 10 selected counties in rural Kenya, who had used at least some form of contraceptive and had experienced at least one childbirth. The analysis employed bivariate analysis using the Chi-square test of independence to identify significant variables (p<0.15) for inclusion in the multivariate analysis. Multiple logistic regression at 95% confidence interval (p<0.05) was then fitted to determine the factors associated with LARC use and unplanned pregnancy. Our findings indicated that partner decision on the current method of contraception was the strongest predictor of LARC use (OR = 5.384, 95% CI = [3.223, 9.275]) among marital status and county of residence. Younger age (15-19 years) was a significant predictor of unplanned pregnancies (OR=3.216, 95% CI= [1.615, 6.281]). Additionally, women residing in West Pokot County were more likely to experience an unplanned pregnancy (OR=2.693, 95% CI=[1.003, 7.624]). The logistic regression models demonstrated good predictive accuracy, with an area under the ROC curve (AUC) of 0.736 for LARC use and 0.799 for unplanned pregnancies. Both models also demonstrated good overall fit as shown by the Hosmer-Lemeshow test (p-value >0.05), suggesting that the models adequately capture the relationships between the predictor variables and LARC use or unplanned pregnancy. All variables had AGVIF values close to one, signifying mild collinearity. Furthermore, cross-validation technique was employed to evaluate the models' predictive performance and generalizability, achieving acceptable average accuracy values (>0.6). These results indicate the importance of targeting educational interventions for LARC use to males. The government should also promote equitable access to family planning services, particularly LARC methods, by strengthening devolved health service delivery at the county level to increase LARC uptake in Nyamira and Kericho counties. Master's Thesis

Determining length of stay patterns in psychiatric Care: a survival analysis approach at Kisumu County Referral hospital

2025-11-11T12:17:36Z

Determining length of stay patterns in psychiatric Care: a survival analysis approach at Kisumu County Referral hospital OCHIENG, Hillary Otieno A key indicator in healthcare management is length of stay (LOS), which measures how long a patient stays in the hospital from the time of admission until they are discharged. Statistics from Kenya National Commission of Human Rights shows approximately 40% of inpatients and 25% of outpatients are affected by disorders in relation to psychological well-being. Kisumu County Referral Hospital (KCRH) is a key provider of mental healthcare services in western Kenya. Nonetheless, there is insufficient data analysis in regard to patient flow and length of stay within the psychiatric unit. This hinders effective resource allocation, capacity planning, and eventually the care standards administered to the victims. The purpose of this study was to ascertain how long mental patients stayed at the Kisumu County Referral Hospital using both survival and regression analysis modellings. Specifically, the research was aimed at fitting Kaplan-Meier model of survival to the data pertaining length of stay for psychiatric patients at Kisumu County Referral Hospital; analyze the impact of covariates on the survival function related to psychiatric patients and compare the Cox regression hazard model with a linear regression model of length of stay for psychiatric patients at Kisumu County Referral Hospital, incorporating covariates to assess differences in predictive performance. The study used monthly secondary data spanning over 60 months between 2018 and 2022, sourced from psychiatric patients’ records from Kisumu County Referral Hospital using a secondary data capture form. On fitting the Kaplan-Meir survival model, the study found that the overall median survival time (time to discharge) was 8 days. No difference was attained in duration taken to discharge males and females (p=0.66). Additionally, the study found that the effect of several plausible interactions such as age and gender, diagnosis and treatment, age and diagnosis but their inclusion was not justified as none of them was significant, the concordance index and Akaike Information Criterion (AIC) only improved by a negligible margin. On comparing the survival model to linear model, the study established that the findings from cox regression and linear regression led to the same conclusions. However, the association with the form of treatment was slightly different. The study concluded that survival analysis models are superior for data sets where survival time is the primary outcome, requiring careful consideration of censoring and time effects. The study therefore suggested that policymakers should promote the use of survival analysis to determine patients’ hospital length of stay. Master's Thesis

Insurance Claim Analysis Using Extreme Gradient Boosting Trees-A Machine Learning Approach

2025-02-11T17:57:12Z

Insurance Claim Analysis Using Extreme Gradient Boosting Trees-A Machine Learning Approach KOLLONGEI, Naomi The emergence of big data has revolutionized the way insurance companies deal with data that they receive in the course of their business, big data involves huge volumes of data of different varieties. Therefore the current methods used for analysis such as statistical methods and actuarial formulas in insurance sector are becoming inadequate to solve the emerging problems and opportunities from advancement in technology. Moreover, the data may be prone to missing values. Extreme gradient Boosting Algorithm (XGBoost) which is an ensemble learning which has the capacity to effectively address the two unique characteristics of the data. This research utilized an Extreme boosting algorithm to process insurance claim data in-order to model the frequency of claim and severity of claims for claim prediction. XGBoost creates tree-based models by iteratively fitting decision trees to the residuals of the previous predictions, effectively reducing the error in each iteration. Using the algorithm we aim to enhance the accuracy of predictions that will yield better estimates for improved risk assessment and pricing of insurance products within the insurance sector. The XGBoost algorithm models were evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Rsquared (RSQ). Results showed that XGBoost models for the claim frequency had a RMSE estimate of 0.949, MAE of 0.7741 and RSQ 0.781 and claim severity model had the metrics 899.12,736.77 and 0.9625 respectively. We also compared the performance of the XGBoost models with zero inflated poisson model, multiple linear regression and generalized Pareto Model. The XGBoost model had the best metrics (RMSE, MAE and RSQ), we therefore concluded that the Extreme Gradient Boosting Model was the optimal model. Key words: Big data, Frequency, Severity, machine learning, gradient boost, XGBoost Master's Thesis

Asset Liability Management (ALM) In Determining Solvency and Profitability: A Case Study of CIC Life Assurance

2024-12-03T14:32:19Z

Asset Liability Management (ALM) In Determining Solvency and Profitability: A Case Study of CIC Life Assurance AOKO, Rose Merab The aim of this research was to analyze the practices of asset Liability Management( ALM) at CIC Life Assurance. The study was significant because it analyzed how ALM practices at CIC Life assurance determined its solvency and profitability. This study’s main objective was to show how ALM determined the solvency and profitability of the company. To determine solvency, solvency and liquidity ratios were calculated while for profitability, ROA and ROE were calculated. The financial ratios calculated helped determine the financial position of CIC Life Assurance. Expected returns were calculated based on past data on beta and risk free rate. Expected returns help make investment decisions. Higher expected returns showed that investors would earn well in their returns and the company would also profit. The project specifically employed Capital Asset Pricing Model(CAPM)to calculate expected return and monte carlo simulation to assess fluctuating economic conditions. Data from January 2018 to December 2022 from the CIC database was obtained and used in the calculation of the ratios. The variables used for analysis were: Total assets, total liabilities, current assets, current liabilities, shareholder equity, net income. The results indicated that CIC Life Assurance is solvent and profitable. Master's Thesis

Quantitative analysis of credit default risk Assessment using black-scholes-merton Model: a case study of the Kenyan Manufacturing industry

2024-12-03T14:21:36Z

Quantitative analysis of credit default risk Assessment using black-scholes-merton Model: a case study of the Kenyan Manufacturing industry AKINYI, Hazel Otieno The Kenyan manufacturing industry is a major contributor of the country’s economy, contributing significantly to GDP growth, job creation, and export opportunities. However, despite its undeniable significance, the Kenyan manufacturing industry is grappling with several challenges that are hampering its growth, with credit constraints being a prominent issue. These challenge often lead to financial distress, forcing some companies to shut down or operate below their optimal potential.This research introduces the Black-Scholes Merton model, an eminent financial tool developed for option pricing, and proposes its adaptation to the context of the Kenyan manufacturing industry. The model is applied to gauge the default probabilities of manufacturing firms by integrating company-specific financial data, volatility, and credit risk factors to assess default risks. The study is based on financial reports published for sampled manufacturing companies in Kenya for the financial years 2016 to 2022. The variables used to compute the probabilities of default are total assets, time period, volatility, debt and risk-free interest rate. The data analysis shows that default probabilities are directly proportional to the company’s liabilities. This research is a comprehensive guide to the assessment, analysis and credit management. Master's Project

A comparative study of cox-ingersoll-ross and Vasicek models: a case study of the 91-day treasury Bill rate in Kenya

2024-12-03T14:16:45Z

A comparative study of cox-ingersoll-ross and Vasicek models: a case study of the 91-day treasury Bill rate in Kenya JEPCHUMBA, Mercy Interest rates is an important factor in the operation of any financial market, with different interest rates having different effects on investment decisions. As such, understanding how interest rates move across different markets can be a crucial factor in managing market risk and maximizing returns. The success of financial investments heavily relies on accurately predicting changes in the rates of interest. The objective of the research was to compare between the Vasicek andCIR model, more accurately captures dynamics of interest rates in Kenya. The reason for choosing these models is they are commonly used because they are analytically tractable and easy to implement. To achieve the objective of this study, we estimated parameters for the models.We compared the performance of both models in predicting future interest rate values. Data on the Treasury bill rates with 91 days maturities was used from the website of the CBK as a proxy of interest rate from July 2019 to September 2023. Parameters were derived using the Ordinary Least Squares technique. An advantage of using the method is that it is easy to implement and handles large data sets efficiently. Microsoft Excel was employed for data simulation. The estimates obtained from both the CIR and Vasicek Models were then used to determine which one better fit the available data, with the research recommending the use of the Vasicek Model due to its stable simulated data and the absence of any significant difference between its test statistics and the actual data. However, caution should be exercised when applying both the Vasicek and CIR models. These findings can serve as a foundation for developing more effective predictive tools for forecasting future interest rate values in Kenya, enhancing the accuracy and robustness of financial analysis and research in this domain. Master's Project

Interest rate risk modeling using semi-heavy tail Distributions of normal variance-mean mixtures: Central bank of Kenya interest rates

2024-12-03T14:11:49Z

Interest rate risk modeling using semi-heavy tail Distributions of normal variance-mean mixtures: Central bank of Kenya interest rates OWINO, Kevin Oduor Derivative prices such as options and bond prices as well as swaps depend on the distributional assumptions of the underlying economic variables, normally, interest rates. The risk associated with changes in interest rates may worsen the value of the contract that depend on it since the values of these assets (derivative contracts) are affected directly by the fluctuations in interest rates. The distribution of interest rates, therefore, needs to be well understood to reduce the risks of losses associated with it. The Binomial Option pricing model assumes that interest rates are constant, with no returns, throughout the life of the option. Another common assumption of the underlying economic variables is that their returns are normally distributed with constant volatility. These assumptions have been used in pricing derivatives and currencies and has led to over-pricing and in some cases under-pricing. These assumptions have been considered inaccurate and misleading. This research uses mixture models exhibiting properties that appropriately capture the peakedness and skewness of interest rates as fundamental variables in pricing. The models of the Normal Variance-Mean Mixtures shows better performance than the normal distribution. The GARCH model is used under the assumption that 91-day Treasury Bills interest rates follow a Generalized Hyperbolic distribution while the Commercial Bank interest rates follows a Normal Inverse Gaussian distribution. A 99pc Value at Risk is then computed for the two models and calculates the minimum expected returns in the subsequent months. This research forms a foundation for the development of advanced pricing models that incorporates the fluctuations of interest rate in the pricing industry. Master's Project

Approximations of ruin probabilities under financial constraints.

2023-06-22T14:45:32Z

Approximations of ruin probabilities under financial constraints. ODIWUOR, Calvine Otieno This thesis studies the approximate ruin probabilities under financial constraints which in- clude the rate of inflation, constant interest rate, and taxation. When the surplus falls below zero, the insurance company is technically considered ruined. The main objective of the study included; to establish a risk model which takes into account all the financial con- straints,to establish analytically, the formula for the approximation of ruin probabilities for both exponentially and sub-exponentially distributed claims, to compare the approximate ruin probabilities from our model and those of the classical Cram´er-Lundberg model, and finally to compare the convergence of Pareto and Log-normal distributions for the formu- lated model. An extensive review of literature is done and much attention is given to the research by Albrecher and Hipp whose research successfully formulates Lundberg’s (classi- cal) risk process in presence of tax. A risk model is formulated in the present study whose premium inflow is influenced by inflation and a constant interest rate. We thereafter in- voke the Albrecher and Hipp loss-carried-forward tax scheme from which an approximation of probability of ruin for the light tailed (exponential) distribution is derived for an exact solution. Then, a suitable formula for the claims with sub-exponential distribution is also derived using the Pollaczek-Khintchine formula. Simulations are hence done using R and Microsoft Excel in this regard. The results show that approximating ruin probability when taking into account all the three financial constraints gives desirable results as compared to those of classical Lundberg model. The comparison between the two heavy-tailed distribu- tions under the concept of limiting density ratio, shows that a Log-normal density exhibit a lighter tail, thus converges faster. However, the model is open for further improvements, specifically to incorporate a stochastic rates of interest. The results of this study will hence guide the policymakers and the insurance industry to make informed decisions to help guard against future ruin as witnessed in local insurance companies in Kenya and globally. Masters Thesis