Statistics and Actuarial Science
https://repository.maseno.ac.ke/handle/123456789/705
2024-03-29T06:27:07ZApproximations of ruin probabilities under financial constraints.
https://repository.maseno.ac.ke/handle/123456789/5738
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
2022-01-01T00:00:00ZForecasting Kenya’s inflation rate using a Varma for price of imported crude oil and Kenya’s previous inflation rate time series
https://repository.maseno.ac.ke/handle/123456789/5233
Forecasting Kenya’s inflation rate using a Varma for price of imported crude oil and Kenya’s previous inflation rate time series
AMISI, Pascal Ouma
Inflation is the persistent rise in the prices of selected goods and services over time.
The rate of inflation measures economic performance of a country and is an important
economic indicator to economists of any given government. High rates of inflation lead to
slow economic growth and has the effect of lowering the living standards of a population
by eroding their purchasing power. In the period November 2016 to June 2017, Kenya
experienced an unprecedented rise in the inflation rate to a high of 11.7% causing harsh
economic and social repercussions to her population [5]. To cushion its population against
such strain, the government should be able to estimate and predict the rate of inflation.
Previous research by Bilal Kargi for Turkey’s case [6] indicates a relationship between the
changes in price levels of imported crude oil and the rate of inflation. The objective of this
study was to determine if there is a long-run relationship between Kenya’s Inflation rate
and the price of imported crude oil, fit a VARMA (p,q) model and use the fitted model
to forecast Kenya’s inflation rate using the previous rates of inflation and the price of
imported crude oil since there was a cointegrated association between the two time series.
This will enable the government plan strategically for the mid- and long-term effects of
inflation in Kenya. Cross-correlation analysis was used to determine whether there is a
significant correlation between the two time series and a test of cointegration was used
to determine a significant association. A VARMA model was fitted to the data using
the SCM approach. The study showed that there exists a moderate negative correlation
between the two time series with a correlation coefficient of -0.21, with a p-value of < 0.05
that implies that the correlation is statistically significant. The study further showed that
there is a moderate statistically significant association between the two time series at lags
6 and that there exists cointegration and dependencies between the price of imported
crude oil and the Kenya’s Inflation rate by a CADF test which a statistically significant
Dickey Fuller Statistic of −8.3394, with a p − value = 0.01, implying cointegrating association
between the two time series. A VARMA (2, 1) model was fitted to the data and
used to forecast Kenya’s inflation rates to six steps (months) behind for comparison to
the actual available data and further a eleven-steps ahead forecast. The forecasts were
accurate with a Mean Absolute Error (MAE) of 0.66% which are good forecasts according
to [17] for planning purposes. From the study results it shows that there exists a
statistically significant association between the price of crude oil and Kenya’s previous
inflation rates and therefore used in forecasting future Kenya’s inflation rates. This study
therefore provides better inflation forecasts(Kenya) to be used for strategical planning for
the mid- and long-term effects of inflation by the government.
2021-01-01T00:00:00ZA correlation study on the effect of Non-conditional cash transfer on poverty Alleviation among older persons in Emuhaya sub- county, Kenya
https://repository.maseno.ac.ke/handle/123456789/5231
A correlation study on the effect of Non-conditional cash transfer on poverty Alleviation among older persons in Emuhaya sub- county, Kenya
MWANIGA, Josphine
The world is experiencing growth in the number of older persons with those aged 60 years and above projected to double from 1.4 billion in 2015 to 2.8 billion in 2050. According to the Kenya Population and Housing Census, there were 1.3 million people who were above 65 years of age in 2009 with a declining mortality rate from 11/1000 in 2007 to 8.93/1000 in 2011 an indication that the number of those aging in Kenya is expected to increase significantly by 2030. In Vihiga County, the population of older persons aged 65 years and above stood at 33,475 by 2013. The growing numbers of older persons in Kenya have increased social, economic and political pressure necessitating introduction of various social protection programs which include non-conditional cash transfer initiatives. Although several studies show that cash transfer programs have a positive effect on access to food, healthcare and shelter, the studies focused on conditional cash transfers creating uncertainty on the effect of non-conditional cash transfers such as Older Persons Cash Transfer (OPCT) on poverty alleviation. This study investigated the effect of non-conditional cash transfer on poverty alleviation among older persons in Emuhaya Sub-County, Kenya. Specifically, the study determined the effect of OPCT on access to food among older persons in Emuhaya Sub-County, Kenya. It also established the effect of OPCT on access to health care among older persons as well as effect of OPCT on quality of shelter among older persons. Case study research design was employed with a target population comprising of 1067 OPCT beneficiaries with a sample size of 290 obtained using Yamane formula which was obtained by simple random sampling and the participants were stratified based on the wards. Descriptive and inferential data analysis techniques were employed to define the participants' characteristics and established the effect of non-conditional cash transfers on poverty alleviation. The study established that there exists a positive correlation between OPCT and access to food with r=0.281 and p- value=0.00. The study also established that there exists a positive correlation between OPCT and access to health care with r=0.120 and p-value=0.004. The study also found a positive correlation between OPCT and access to a quality shelter with r=0.162 and p-value=0.000. The odds ratio predicted by the model for improved access to food, health care and quality was 1.534, 2.388 and 1.793 respectively. The study concluded that OPCT alleviates poverty. The recommendation for the study was that a large sample size should be considered to access poverty alleviation among the older persons on the OPCT program. Secondly since household size differ, this affects the quantity of food from the household and therefore the cash provided should put this in mind to ensure that the household have improved food access. Lastly, improved access to health care had a weak correlation with cash transfer and in order to strengthen the correlation the government should pay NHIF for all beneficiaries and not a sample.
2021-01-01T00:00:00ZSimplifying the markov chain analysis of rainfall Data using genstat
https://repository.maseno.ac.ke/handle/123456789/5196
Simplifying the markov chain analysis of rainfall Data using genstat
ONG' ALA, Jacob Otieno
Despite the rapid development of statistical packages, a lot of climatic data still remain
unanalyzed due to lack of specialized routines in most of the packages, One package has a
climatic menu though with limitation on complex analysis such as generalized linear models.
Others can perform the Generalized Linear Model analysis but do not have a specialized menu
for analyzing climatic data. There is no statistical package currently available which has a
specialized capability to do climatic analysis easily and includes the use of generalized linear
models. This study starts the work of creating a specialized menu in GenStat for analyzing
climatic data by implementing Markov modeling of rainfall data. Four procedures have been
written and corresponding dialogues were created to ease their use. Incorporating a climatic
menu into GenStat package will support researchers in agricultural and many other fields that
need an analysis of climatic data as part of their work .
2011-01-01T00:00:00ZDeterministic modelling of tuberculosis and Hiv/aids
https://repository.maseno.ac.ke/handle/123456789/5195
Deterministic modelling of tuberculosis and Hiv/aids
ODUNDO, Francis Okello
The human immunodeficiency virus (HIV) pandemic presents ~ massive challenge to the
control of recurrent diseases like tuberculosis (TB) at all levels. Tuberculosis is also one of the
most common causes of morbidity and one of the leading causes of mortality in people living
with HIV/AIDS (PLWHA).
In this study, we have developed a mathematical model that captures the role played by
HIV/AIDS in accelerating the infection and hence spread of Tuberculosis. We looked at TB
progression among people with HIV and those without. The model is formulated for TBIHlV
negative individuals as well as for TBIHlV positive people. The model was developed using
the first order partial differential Mackendrick- Yon Foster equation.
Further, we reviewed different epidemiological techniques to estimate parameters in the model.
These parameters were estimated through extraction of relevant information from data
available in the literature. Finally, we were able to present computed numerical solutions of the
model using MATLAB.
2010-01-01T00:00:00ZEfficiencies of reinforced bib and augmented· Block designs in sugarcane test families’ vs Controls experiments
https://repository.maseno.ac.ke/handle/123456789/5188
Efficiencies of reinforced bib and augmented· Block designs in sugarcane test families’ vs Controls experiments
MAINA, Peter Wachira
The designs used for experimentation generally require making all the possible paired
comparisons among the treatments but in plant breeding selection programmes the
comparison of interest is usually a subset of all the possible paired comparisons.
These comparisons are usually between the new varieties and commercial varieties
called control varieties. These designs for test versus control experiments when the
test treatments contain homogeneous material, such as mass selection in sugarcane
breeding, have received adequate attention. Breeders in sugarcane breeding
programmes have shifted from mass selection to family selection where the test
treatments are more heterogeneous. This shift has created a need for efficient
experimental designs to evaluate hybridized sugarcane families. In this study we
evaluate two designs, Augmented Block Design (ABD) and Reinforced Block
Incomplete Block Design (RBIBD), which have been proposed for test versus control
experiments though their efficiencies in test families versus control experiments are
not known. To evaluate the designs, we simulated data for five families and two
controls through Monte-Carlo simulation framework. RBIBD and ABD designs were
constructed and data fitted by inclusion of block effects and random errors. The fitted
data was then analysed and compared the Randomized Complete Block Design
(RCBD). More concrete results in this area could improve the efficiency of sugarcane
selection process which would be of great benefit to the stakeholders in the sugar
industry.
2010-01-01T00:00:00ZNon-parametric regression estimation of a finite Population total in the presence of Heteroscedasticity
https://repository.maseno.ac.ke/handle/123456789/5183
Non-parametric regression estimation of a finite Population total in the presence of Heteroscedasticity
INGUTIA, K. Celestine
Non parametric regression provides computationally intensive estimation.of unknown
finite population quantities. Such estimation is usually more flexible and robust than
inferences tied to design - probabilities (in design-based inference) or to parametric
regression models in (model-based inference). Dorfman [9] used a more general super
population model to find a non-parametric regression based estimator for the population
total T . He, however, assumed homoscedasticity when constructing his proposed
estimator. In his empirical study, he noted that the data showed clear signs of
heteroscedasticity. In this study we consider the improvement in the efficiency of
Dorfman's non-parametric regression based estimator of a finite population. To do this
we incorporate a reasonable assumption of variance structure into the non-parametric
regression methodology and use the weighted least squares method to obtain the
proposed non-parametric regression based estimator. In our empirical work we have used
two kinds of data sets: simulated and secondary data. The simulated data is of two kinds:
homoscedastic and heteroscedastic generated with the help of Genstat 8th edition
statistical application package. The secondary data was obtained from the internet from
the United States Bureau of Labor Statistics. By calculating Dorfman's and our
population estimates based on the given data sets using Dorfman's and our proposed
estimator's respectively, we have established that our proposed estimator is more
efficient than Dorfman's, that is, the efficiency of Dorfman's non-parametric regression
based estimator has been improved when we put into account heteroscedasticity.
2010-01-01T00:00:00ZThe Use of Cast Tests and Exercises to Improve The Learning of Statistics at Tertiary Level of Education
https://repository.maseno.ac.ke/handle/123456789/5122
The Use of Cast Tests and Exercises to Improve The Learning of Statistics at Tertiary Level of Education
MANYALLA, Benard Odhiambo
Statistics as a course has become a computerised teaching subject due to the changing needs
of the students who often use computers to process, and analyse various data sets. Recent
technological developments have led to the avai labi Iity of resources of the highest qual ity for
Statistical teaching, including Computer Assisted Statistics Textbooks \CAST). The purpose
of this study was to illustrate the added benefit of using an interactive quantitative method of
teaching Statistics over the historical usual classroom teaching at the Kenya Institute of
Management (KIM). As part of the objective, this study attempted to conduct educational
experiments at different times with different students leading to a quantitative analysis where
potential confounding effects are demonstrated and adds rigor to the study using convenient
sampling without compromising student's education. This study was conducted at KIM over
a period of nine months. Past results on Statistics course obtained by the students taught by
researcher(Manyalla) and colleague teacher(Margaret) before CAST usage were compared
with results obtained when CAST was used in the teaching of Statistics. A total of 167
students were investigated in this study as having used CAST or not. Out of these, 77
Statistics students were taught using CAST while 90 were taught with the use of the
traditional method. An analysis of past Statistics' results data showed that the marks were on
average about 10% higher than the average marks our students were getting before using
CAST. Overall, the average mark for the 90 students who did not use CAST was 59%, and
this was close to the national average of 57% in Statistics course. It was just over 70% for the
77 students who used CAST. Future studies are needed to determine the effectiveness of
CAST for professional education and training in Statistics department from the various KIM
branches and in other institutions where Statistics module is offered.
2012-01-01T00:00:00ZAnalysis of seasonal time series with Missing observations: A case of harvesting of fish in Lake Victoria Kenya.
https://repository.maseno.ac.ke/handle/123456789/4052
Analysis of seasonal time series with Missing observations: A case of harvesting of fish in Lake Victoria Kenya.
OTWANDE, Andrea
ABSTRACT
Time series is a measured observation recorded with time. This statistical procedure
is applicable in many fields of study including engineering and economics. The process of
collecting data sometimes faces a lot of challenges that may arise due to defective working
tools, misplaced or lost records and errors that are prone to occur. These problems can be
addressed by estimating the missing values so as to enable one to proceed with the analysis
and forecasting. The most commonly used approaches include the use of autoregressivemoving
average models developed by Box Jenkins, use of extrapolation or interpolation
under regression analysis and use of state space models where data is considered as a
combination of level, trend and seasonal components. This project intends to use the most
appropriate method of estimating missing values by using the direct method of imputation.
Incomplete secondary data obtained from the Ministry of fisheries and Development,
together with the Kenya Marine and Fisheries Research Institute are to be used to estimate
the gap left just before, during and immediately after the post election violence of the
year 2007/2008, a time when data could not be obtained and/or recorded. The original
time series data when analysed produced a SARIMA model (0,1,1)(2,0, 0h2 as the best
candidate for the lower segment. SARIMA (0,1,2)(0,0,1)12 was produced for the upper
segment using autoarima function in R package. The missing data were estimated using
forecast from the lower segment which was extended to the in sample forecast in the upper
segment. The regression test between predicted and the original values in upper segment
proves strong positive relationship indicating high level of accuracy on predictability of
the model used.
2013-01-01T00:00:00ZMultilevel Analysis Applied to Binary Data: Malaria Prevalence in Sauri Millenium Village, Kenya
https://repository.maseno.ac.ke/handle/123456789/3710
Multilevel Analysis Applied to Binary Data: Malaria Prevalence in Sauri Millenium Village, Kenya
LELERAI, L. Eliud
Millennium Villages Project is an initiative that is meant to demonstrate that the millennium
development goals could be achieved in an integrated approach in putting a combination of
interventions in place. Among these interventions are the health interventions of reducing the
prevalence of common diseases. Malaria is one of these common diseases. In 2005 Sauri
Millennium Village was started in western Kenya which was then followed by 13 other villages
across Africa. A baseline study was done in 2005 to measure the bench marks of the millennium
development goals indicators in the village. As part of these surveys, blood data was collected to
estimate the baseline prevalence of malaria in the Sauri Millennium village. This data was linked
to socioeconomic data to study factors affecting malaria prevalence. Malaria affects individuals
who are clustered in households and villages. In addition to individual effects, households and
villages have characteristics that influence malaria prevalence. The individual characteristics
under study were age and gender. The household characteristics were income and the education
status of the household the individual belongs. The village level factors were the counts of water
.
bodies and the area covered by woods of the villages. Logistic regression models were applied to
understand the determinants of malaria. Considering the multilevel structure of data, the analysis
goes beyond the single-level modelling and explores the value of multilevel modelling in
understanding the malaria risk factors. The analysis showed that malaria prevalence among the
population at baseline was about 50% and was similar for males and females. The results also
showed that malaria prevalence decreases with age. Income and education status of the
households were also found to have an effect on malaria prevalence. The utility of the multilevel
techniques in answering the research questions clearly demonstrated the value of statistical
techniques in understanding factors affecting health outcomes. The recognition of complex
structures of data in statistical modelling processes, yield reliable results that help health
strategists make informed decisions in taming malaria.
2014-01-01T00:00:00Z