MST-Department of Statistics and Actuarial Science

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    A Continous-Time Optimal Investment and Consumption Strategy for Commercial Banks under the Hamilton-Jacob-Bellman Optimization Technique with Bounded Interest Rates
    (Kenyatta University, 2021) Chepng’eno, Rono Daisy; Ananda Kube
    The CIR model is used to model interest rates in this project, which analyses an investment and consumption problem under bounded interest rate conditions. Our goal is to determine the optimal investment and consumption strategy to maximize predicted utility of consumption and terminal wealth. To begin, we build the HJB equation for the value function using the dynamic programming approach, and then complete our analysis using the logarithm utility. Second, by conjecturing the shape of a solution and solving partial differential equations, we build closedform solutions to the optimal investment and consumption strategies. Finally, we present a numerical example that demonstrates how market variables influence the best investment and consumption strategy.
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    Estimation of the Population Variance Using a Smoothing Operator Under Simple Random Sampling
    (Kenyatta University, 2019-06) Odhiambo, Lavender Akoth
    Variance estimation has been a major concern in sample survey theory. The problem in estimation theory is to determine estimators that have smaller variance under a given model speci cation. However, existing variance estimators su er from boundary problems and outlier sensitivity. To address this, a robust variance estimate of the ratio estimator of the population mean using a multiplicative bias correction technique under model based approach is considered. Asymptotic properties of the robust variance estimator are investigated. Also a comparative study of the existing variance estimators and the derived robust variance estimator of the population mean is studied. The results of the study show that under mild assumption, the derived variance estimator of the population mean is asymptotically more consistent and has a better coverage probability as compared to rival variance estimators of the population mean.
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    High-risk sex practice and its determinants among HIV-positive women on HIV care services: a case of Thika level 5 hospital, Kiambu, Kenya
    (Kenyatta University, 2014) Musyoka, Tobias Matano; Kahiri, J.M.
    HIV/AIDS remains a major health issue in Kenya and in the whole world. Over 34 million people are currently living with the HIV and a majority of them are in the Sub-Sahara Africa; a big pool for potential HIV transmission. In Kenya, out of a population of 40 million, over 1.6 million are HIV infected and approximately 100,000 new infections are realized yearly, most of them through unprotected sexual intercourse. This study sought to estimate the prevalence of high-risk sex and to identify its determinants among the HIV-positive women undergoing HIV care in Thika Level 5 Hospital. A total of 467 participants were drawn through systematic random sampling from the population of HIV positive women attending HIV care services. Data was collected from those who passed the inclusion and exclusion criteria by using face-to-face interviews. The data was analyzed using Statistical Package for Social Sciences (SPSS) where descriptive statistics and inferential statistics were computed. The results showed that high-risk sex is prevalent among the HIV-positive women undergoing care as 39% of the respondents reported not to have used condoms during their last sexual activity. Disclosure of HIV status, Relationship control, Time on ART, Drugs use, and Stigma in bivariate analyses was significantly associated with high-risk sex at the significance level of 0.05. In the multivariate analysis the variables Time on ART, Partner type and Disclosure*Stigma interaction term remained significant in predicting high-risk sex. The study associated long Time on ART to high-risk sex. Casual partnerships were 7 times associated with high-risk sex than regular partnerships. A combined Non-disclosure and Stigma influenced high-risk sex practice two-fold. The study concluded therefore, that the determinants of high-risk sex among the HIV-positive women on care are long time on ART, Casual or mixed sexual relationships, Stigma, and Non-disclosure. The study recommended that the PLHIV should be given the right preventive information and be cautioned that being on ART for long is not a permit to stop using condoms. Stigma coping-skills training should be given to the patients and be made to accept and live with their condition without transmitting the virus to others. The government and the donor community have also been urged to provide resources to help develop interventions that reinforce safe sex practices and also put up infrastructure for improving the socio-economic conditions of the PLHIV
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    Maximum Likelihood Estimation of Parameters For Poisson-Exponential Distribution Under Progressive Type I Interval Censoring
    (Kenyatta University, 2020) Situma, Peter Tumwa
    The problem of estimating the parameters of Poisson-Exponential distribution under progressive type-I interval censoring is considered. Previously, researchers have considered maximum likelihood estimation under the progressive type-I interval censoring scheme for various distribution, but no research has considered Poisson-Exponential. Poisson-Exponential is a two-parameter lifetime distribution having an increasing hazard function. It has been applied in complementary risks problems in latent risks, that is in scenarios where maximum lifetime values are observed but information concerning factors accounting for component failure is unavailable, which can be experienced in fields such as public health. Under progressive type I interval censoring, observations are known within two consecutively prearranged times and items would be withdrawn at pre-scheduled time points. Progressive typeI interval censoring scheme is most suitable in those cases where the continuous examination is impossible. Based on progressive type I interval censored data, the Maximum Likelihood Estimates of Poisson-Exponential parameters are obtained via the Expectation-Maximization algorithm. The Expectation-Maximization algorithm is preferred as it has been confirmed to be a more superior tool when dealing with incomplete data sets having missing values, or models having truncated distributions. In this study, the estimates derived are compared through simulation based on bias and the mean squared error under different censoring schemes and parameter values. It is concluded that for an increasing sample size, the estimated values of the parameters tend to the true value. Among the four censoring schemes considered, the third scheme p(3) provides the most precise and accurate results followed by p(4), p(1) and lastly p(2)
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    Maximum Likelihood Estimation of Parameters of Lomax Distribution Based on Progressive Type-II Hybrid Censoring Scheme.
    (Kenyatta University, 2018) Mwendwa, Peace Mwende
    Lomax distribution is an important lifetime distribution. The process of obtaining estimates of parameters for di erent lifetime distributions under various schemes still remains an area of interest. In Lomax distribution, parameter estimates have been obtained using ordinary procedures like Newton Raphson when the test units follows a progressive Type-II hybrid censoring scheme whereby within most cases the obtained values do not converge easily to the true value. The MLEs are observed to be generally di cult to obtain in a closed format. As a result, we recommend to employ EM algorithm procedures in order to attain the MLEs of the parameters of Lomax distribution build onto progressive Type-II hybrid which amalgamates Type-II and hybrid censoring schemes. Performance of these obtained MLEs is compared with those obtained using NR methods and EM algorithm for di erent censoring schemes with regard to their mean bias and MSE at xed parameter values of and . Simulation studies reveal that the MLEs via EM algorithm performs better than those obtained via NR method. The results of the obtained estimators are illustrated on real data.
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    Robust M-Estimators of the Population Mean.
    (Kenyatta University, 2018-07) Mutuguta, Bernard Githui
    Valuable information may be contained in outliers. Data collected from many medical equipment such as the ECG time-series may result in unusual patterns, a situation that may represent disease conditions. Some outliers may therefore provide an insight into crucial information that may lead to the discovery of new knowledge.Due to the di culties involved in the study of outliers, majority of current research works have chosen not to out-rightly reject the outliers but have adopted methods that accommodates them but have their in uence reduced to some degree. This has resulted in the development of estimation and testing techniques that have yielded robust estimation. Three robust M-estimators (the Huber, the Hampel and the Tukey's biweight) were adopted in this paper with an aim of comparing their e ciency in the estimation of population mean in an asymmetrical distribution. Simulation was used to generate a normal population which was then contaminated with a few outlying observations. A simple example illustrated how the comparison of the M- estimators was carried out on real data. On the basis of the ndings from this research, the M-estimator that turned out to be the best, was the Tukey's biweight followed by the Hampel's and the Huber's was the weakest of the three. However all the three M-estimators yielded unbiased estimates of the population mean.
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    Seasonal Naïve Model Incorporating Trend Component for Tax Revenue Forecast in Kenya
    (kenyatta university, 2023) Samuel, Fredrick Kyalo; Titus K. Kibua
    Tax revenue is largest source of government revenue in Kenya. Nevertheless, the tax revenue collection has overtime fell below the planned targets. Besides, Kenya has witnessed continuous increase in public debt since public expenditures have maintained consistent growth pattern and continually surpassed revenues. The structure of tax revenue data in Kenya exhibit seasonality fluctuations with progressive increase (trend) in monthly tax revenue collections of the year. In order to facilitate government in proper fiscal planning and long-term projections, modelling and forecasting tax revenue is desirable. The objectives of this study were to develop a seasonal naïve model incorporating the trend component for forecasting tax revenue in Kenya and use the model to forecasting tax revenue collections in Kenya for the next two years. This research used time series approach to build the model. The monthly tax revenue data comprising of 192 months spanning July 2000 to June 2016 was used in this study. The study found that seasonal naïve model with trend was appropriate model for forecasting tax revenue data since it recognized both seasonal and trend components in the data and recommended application of the developed model in forecasting tax revenue collections in Kenya. Modelling the causal relationship of tax revenue with other variables that account for seasonality such as inflation, exchange rates, public expenditure and public debt was identified for future area of study.
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    A Statistical Application of Regression Analysis to Investigate and Determine the Factors That Influence the Uptake of Family Planning in South Imenti Sub County - Meru County
    (kenyatta university, 2023) Mpuria, Thomas Bundi; James Kahiri
    Family planning is one of the mitigation factors adopted by the Kenyan Government in achieving its strategic development goals through reducing child mortality and maternal mortality, thwarting unwanted pregnancies, prevention of STDs, promoting education and the economic empowerment of women. Despite many advantages of family planning, its utilization and adoption in Kenya is 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 existence of family planning methods, lack of information about various forms of family planning methods, negative attitude toward some family planning methods due to lack of counselling/sensitization to mothers on their side effects, difficulty 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 being offered free of charge in all government clinics. Statistics from the recent census done in the year 2019 indicate that there are more young girls aged between 15-24 years with children, which indicates that teenage pregnancies are rampant. This implies that the uptake of family planning resources is still very low despite numerous sensitization programs. The goal of this study was to apply binary logistic regression method to examine factors that impact on the usage of family planning methods in South Imenti sub-county. The target population was 9,900 women between the ages of 15 and 49. A total of 385 mothers were chosen using stratified simple random sampling 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 binary logistic regression model on the data collected showed that age, education level, marital status, number of children and frequency of mothers in following media were potential explanatory variables that have a significant effect on the utilization of family planning practices.
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    A Statistical Investigation to Determine the Predisposing Risk Factors for Predicting Prevalence of Active Tuberculosis in North Pokot Sub County, West Pokot County, Kenya
    (Kenyatta University, 2018-10) Mboga, Lydia Nyabate
    Tuberculosis is a major threat to world health. Finding out the TB cases and treatment of the disease are the tenet means of controlling TB transmission and reducing its incidence. In many industrialized countries, the prevalence of tuberculosis has declined significantly in the last decade, and elimination of TB has come back as a foreseeable goal, based on efficient treatment of overt TB cases and treatment of latent TB infection to prevent development of the disease. In developing countries, however, the number of TB cases is reported to increase steadily, especially in Africa South of Sahara, where TB is a leading cause of mortality. TB disease burden in Kenya is large and rising. Kenya is ranked 13th out of the 22 countries which collectively bring about 80% of TB cases in the World. It affects all age groups but more so the economically productive age group of 15 and 44 years. Few studies have considered the risk factors for tuberculosis at community level in highly resource-poor countries. The study was conducted in Kacheliba Sub-County hospital in West Pokot County. The aim of the study was to investigate and determine the predisposing risk factors for predicting the prevalence of active tuberculosis in the region. The study design which was employed was analytical cross sectional design targeting all persons above 15 years and children of 0-14 years. Hospital records and questionnaires were used in collecting data. Chi-square and Fisher’s exact tests at 5% level of significance were used in comparing pulmonary tuberculosis prevalence between subgroups in r × c tables. A Logistic regression model was used to determine the significant factors for predicting tuberculosis in North Pokot Sub-county. The study findings indicated that tuberculosis prevalence in North Pokot Sub-county was higher than the national prevalence; 9/1,000 and 2/1000 respectively. The logistic regression model indicated that, alcoholism, smoking and congestion as being statistically significant factors in predicting tuberculosis in North Pokot Sub-county. The study findings will be used by community health care workers in creating awareness among community members on predisposing factors for tuberculosis and on the need to sought medication early to avoid complication of the disease and further transmission.
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    A statistical study of factors associated with psychosis at Mathari Hospital, Nairobi
    (Kenyatta University, 2015-11) Olwende, Wilfred Musanda
    Although there are known factors associated with increased risk of developing psychosis, the exact etiology remains elusive. Psychosocial and biological factors are known to interact in their development. Factors such as obstetric complications, season of birth, drug abuse, migration and ethnicity, urbanicity, social adversity, and trauma in childhood have been found to be related to psychosis. Unfortunately, studies done in Kenya only look at these factors as secondary to other inquiries. This study sought to identify the determinants of psychosis as presented by patients admitted at Mathari Hospital. Mathari Hospital is Kenya's sole National Referral and Teaching psychiatric Hospital with a capacity of 700 beds. This was a cross-sectional study of patients being discharged from Mathari Hospital at the time. A questionnaire was designed to help in collecting information from the patients, after obtaining permission from the Kenyatta National Hospital/ University of Nairobi Ethics and Research Committee. First patient was randomly selected, from a list of patients admitted at the time, after which every odd number patient being discharged was approached for interview. The patient included was to be able to respond to questionnaire items. Agitated patients were excluded. Clinical notes at admission were incorporated for clinical history, as well as primary caregiver accounts. Data analysis was performed in R 3.0.2 Software. Data obtained was analysed in terms of descriptive statistics, and later logistic regression was used to determine the important factors that affect psychosis and establish any associations that are unique to the Kenyan scenario. Multiple linear regression was used to establish factors that determine length of DUP. One-way ANOVA was used to test the effect of social and biological factors on DUP and age at onset of psychosis. Simple linear regression was done to model the relationship between age at onset 'of psychosis and duration, in years, of drug abuse. A total of 145 patients completed the interviews. Majority of the respondents were male patients (55.17%, n=80, N=145). 53.79% (n=78, N=145) of the respondents had a working diagnosis of psychosis. The mean age at onset of psychosis was 26.03±7.67 SD (n=67, N=145), the mean Duration of Untreated Psychosis (DUP), in weeks, was 10.19±8.47 SD (n=67, N=145). It was established that family history of psychosis and residence were significant in predicting the probability of a patient having psychosis. Drug abuse and residence were significant in determining the length of DUP.