Master Dissertations

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Actuarial modelling of severity claims in motor insurance by fitting probability distributions: a case of Dar es salaam
(The University of Dodoma, 2017) Nganzi, Erick
The purpose of this study was to find out the appropriate probability distributions that fit suitable to the motor insurance claims in respect of motorcycles, cars, and heavy vehicle insurance claimed amounts. The specific objectives were: to estimate the probability distributions considered, to identify appropriate model that fit best to the motor insurance claims amounts among eight distributions and to test the goodness of fit of the fitted probability distribution models. Daily data were collected from Britam Insurance Company Limited (T) from January 2007 to December 2016 of Dar es Salaam region. The estimates of parameters of the distributions were obtained by using maximum likelihood estimation method, and Kolmogorov-Sminov test statistic was used to fully assess the goodness of fit of eight probability distributions considered at 5% level of significance. Appropriate probability distribution model has been identified based on model selection criteria developed. Empirical Distribution Function (EDF) and Cumulative Distribution Function (CDF) plots were also used to visually assess the goodness of fit of the distribution models. The log likelihood values and Akaike’s information criterion were obtained and used as the selection criteria of the model that fit best the motor insurance claimed amounts. The model with large log likelihood value was considered to be the better model or the model with minimum AIC was considered to be the better model for motor insurance claimed amounts. These data were analysed by using SAS version 9.4, and SPSS version 21. The results showed that the Lognormal distribution fitted best to the motorcycle insurance claimed amounts and Inverse Gaussian distribution model fitted best to the car and heavy vehicle insurance claim amounts respectively.
Anisotropic neutral models with van der waals Equation of state
(The University of Dodoma, 2017) Mahali, Kasongo Andefise
We find new exact solutions to Einstein-Maxwell field equation for neutral anisotropy stellar stars with Van der Waals equation of state. We adopted Sunzu, Maharaj and Ray‘s metric function and measure of anisotropy. The solutions are obtained after considering the transformed Einstein-Maxwell field equations for neutral anisotropic matter. In our models, we regain previous anisotropic and isotropic results as a special case. We consider the space-time geometry to be static spherically symmetry. The exact solutions to the Einstein-Maxwell field equations corresponding to our models are found explicitly in terms of elementary functions namely simple algebraic functions. The gravitational potentials and matter variables generated are well behaved. We also generate relativistic stellar masses consistent with the stars PSR J1614-2230, Vela X-1, 4U 1538-52, LMC X-4, SMC X-4, Cen X-3, Her X-1, SAX J1808.4-3658 and EXO 1785-248.
Blow-up of solutions to problems for nonlinear hyperbolic equation.
(The University of Dodoma, 2016) Chillingo, Josiah Kidney
Different physical phenomena can be represented in terms of nonlinear problems for partial differential equations; however such problems are often subjected to singularities. Thus it gives rise to a permanent research interest to such problems. In the present study we provide reviews of essential approach applied to Cauchy problems and initial-boundary problems for hyperbolic equations based on latest results in this ﬁeld.
Carleman estimates to solutions of direct and inverse problems for hyperbolic equations
(The University of Dodoma, 2015) Ngomaitala, Hussein Rajabu
A number of phenomena in modern science can be conveniently described in terms of problem for hyperbolic equation with Carleman estimates to the solution of inverse problem. The purpose of this study is to give a survey of the solution of the inverse problems for hyperbolic equation by Carleman estimates. We extend the results and prove the Carleman estimate focusing on an inverse problem for a simple hyperbolic equation. Also we derive the Lipschitz's stability by energy estimate; we obtain tomographic images by sent x-ray in different directions and measured at different places.
Comparing evaluation methods of students’ performance in secondary schools in Mbulu district using statistical quality control grade and fixed grading
(The University of Dodoma, 2022) Alphonce, Filbert
Tanzania like other countries in the world is faced by challenges in secondary education system. There is enough evidence that, assessment of students’ performance is one of the challenges that face assessors in secondary schools. Despite the mitigations agreed to solve the challenges on evaluation of students’ performance in the country. Studies about evaluation of students’ performance that have been conducted in Tanzania have mainly focused on fixed grading method. To fill this gap, this quantitative study investigated students’ performance by comparing their performance using statistical quality control charts grade and fixed grading method. The study is guided by three specific objectives which were: to assess students’ performance of a subject by using individual control chart over fixed grading method, between subjects by using mean and S control chart over fixed grading method and within a school by using group control charts over fixed grading method. The study was conducted in ordinary secondary schools in Mbulu District. It employed secondary data which were collected from240 students’ sampled documents obtained from academic students’ progressive report from six ordinary secondary schools in Mbulu District. The students’ performance was analyzed as per specific objectives by using Minitab Statistical Software with the help of statistical quality control charts grade and fixed grading method. After the analysis of the collected data, the quality control charts grade revealed that more students were performing well as compared with the analysis done by fixed grading method. The findings implied that statistical quality control charts grade was a tool that caused a large number of students to pass their examinations as opposed to the fixed grading method in evaluation of students’ performance. This is because the statistical quality control charts grade lower the cut-off points of the students’ performance. These findings have an implication in evaluating students’ performance since secondary school teachers may use statistical quality control charts grade to increase individual students’ performance in each subject.
Comparing the logarithmic least square and eigen value methods in analytic hierarch process by using the best job example.
(The University of Dodoma, 2016) Revocatus, Ponsian
This dissertation centers on comparing two methods based on consistence and ranking preservation of alternatives in analytic hierarchy process (AHP) by using the best job example. These two methods logarithmic least square method (LLSM) and eigenvalue method (EM) are used to develop approximations of ratio scales from a positive reciprocal matrix. The measurement of consistency and rank preservation are the main criteria for comparison of these two methods. The priorities obtained for each method from the combination of the comparison matrices for all criteria with respect to all alternatives, the ranking of the alternatives were given against the four covering criteria, the results show that, the two methods namely LLSM and EM give different results on ranking the alternatives as shown by Saaty and Vargas(1984).
The contribution of teaching aids (counting objects) in numeracy skills performance for standard two pupils: a case of Kiteto district
(The University of Dodoma, 2017) Mkonyi, Sarael Jonas
This study aimed at investigating the contribution of teaching aids (counting objects) in numeracy skills performance for standard two pupils. The main objective of this study was to introduce an effective intervention for enhancing pupils’ achievement levels in numeracy. The study revealed that there is a low numeracy skill which is caused by many reasons such as unsuitable teaching and learning environment, few teaching methods, negative attitude of pupils and parents towards numeracy, shortage of teaching and learning materials, negative interaction between teachers and pupils to mention few. Pupils who experience learning difficulties are not having low numeracy skills; rather the teaching methods may be the result of their low numeracy skills. This study uses qualitative and quantitative approaches. The study used purposive sampling and simple random sampling whereby purposive sampling used to select eight (8) teachers in eight (8) different schools who teach numeracy in standard two to fill the questionnaires and simple random sampling was used to select forty (40) pupils from four (4) schools (ten (10) pupils from each school) for focus group discussion (FGD). Data were collected through questionnaire, focused group discussion, observation and documentary review. The data obtained were analyzed and interpreted through short statements and other studies from different literature for qualitative data and Microsoft Excel for quantitative data. The study revealed that teaching aids used in teaching and learning numeracy are locally made; some of the teachers use it frequently and effective use of teaching aids in numeracy skills increases performance.
Demographic factors influencing the prevalence of HIV/AIDS in Mbeya region of Tanzania
(The University of Dodoma, 2017) Edward, Noel
This study is conducted in the aim to figure out the demographic factors that fueling prevalence of HIV/AIDS in 2011/2012-Mbeya region. Demographic data of the cross-sectional years 2011/2012 is used. The data encompass male and female individual age group of 15-49.The binary logistic regression model was employed and demographic factors that were considered to have an impact on the prevalence of the epidemic were included in my analysis. The result shows that demographic variables had significant effect on the prevalence of HIV/AIDS in the year 2011/2012-Mbeya region for all respondents. However, except for male circumcision for male individual, polygamous, travelers and pregnancy status for female individuals, the demographic parameters such as respondent’s age, respondent’s sex, place of residence, paid sex (commercial sex), and unsafe sex, had significant effect on the prevalence of HIV/AIDS in the year 2011/2012 in Mbeya region.
Design of sampling plan in terms of acceptable quality level (AQL) and sustainable quality region (SQR)
(The University of Dodoma, 2017) Kuhanga, Seleman Dominicus
Attribute sampling plans on quality indices like AQL and MAPD gives the way for Sustainable Quality Region SQR=MAPD-AQL especially for the product at initial stage of production, where the exact quality of the product was not well designed. Optimum information on Acceptable quality level (AQL) and Maximum allowable percent defective would be better for protecting both consumer and producer in terms of SQR along with AQL or MAPD. New single sampling plans were developed by suggesting a unique monotonic increasing function on operating ratio(R) based on SQR with either AQL or MAPD corresponding to acceptance numbers. This study suggests a new quality region called Sustainable Quality Region (SQR) which exceed AQL and precede MAPD. ie proportional defective falls between AQL and MAPD ( SQR ), ie SQR= ( MAPD-AQL). Also, optimum sampling plan was suggested by establishing the measures AQL and MAPD, which are more producer and consumer friendly. The OC curves of SQR plans were compared with other AQL plans. Another single sampling plan was developed by considering the relationship between the MAPD with SQR so as to obtain the quality level that will protect consumer from getting the product with poor quality. Also economic SSP was developed based on MAPD –Min(ATI) at AQL and SQR-Min(ATI) at MAPD which aims for developing the quality level that both consumer and producer will be protected from getting poor quality product (consumer’s risk) with minimal cost of inspection as well as high quality items not to be rejected (producer’s risk). Also interesting relationships of SQR with AQL, MAPD, LTPD, TQR, AOQL and MAAOQ were presented so as to evaluate the other quality indices of the prescribed and suitable examples were illustrated.
Effects of chemical reaction on an unsteady hydromagnetic natural convection flow of a rotating and radiating fluid past a vertical porous flat plate in the presence of heat sink
(The University of Dodoma, 2018) Asegelile, Alex
The objective of this study is to investigate the effects of chemical reaction on an unsteady hydro - magnetic natural convection heat and mass transfer ﬂow of incompressible, vis-cous, rotating and radiating ﬂuid past an inﬁnite vertical porous ﬂat plate in the presence of heat sink. The Rosseland approximation is used to describe the radiative heat ﬂux for optically thick ﬂuid in the energy equation. The system of non - dimensional partial differential equations governing the ﬂow has been solved numerically by applying the Ritz ﬁnite element method. The effects of the various physical parameters describing the ﬂow transport are discussed for Grashof number (Gr > 0), corresponding to cooling of the plate, and Grashof number (Gr < 0), corresponding to heating of the plate. Numerical data for the skin - friction coefﬁcient, Nusselt number and the Sherwood number presented in the tables and then discussed. Keywords: MHD, natural convection, magnetic ﬁeld, rotating ﬂuid, optically thick ﬂuid.
Evaluation of secondary schools students performance in Igunga district by using statistical quality control methods
(The University of Dodoma, 2018) Zacharia, Charles
In Tanzania secondary education, evaluating of students’ performance is a problem. In this study, students’ academic performance from six secondary for four years were assessed by using Statistical Quality Control (SQC). Data collected for the study, were secondary data from academic documents which were students’ progressive report. Statistical quality control charts were used to analyze data collected. After evaluating out of 14 of Individual control charts, 12 charts were found to be out of statistical control. Out of the 19 of mean control charts all 19 charts were out of the statistical control. For the group control charts indicated that out of 6 charts all 6 out of them also, were out of the statistical control. Therefore, secondary school students’ performances were shown to be out of statistical control, which implied that, there were assignable courses of variations operating in the students’ performance, which should be detected and corrected. However, if students’ performance for the four years of study fell within the control limits, then we could conclude that the students had maintained the desired target performance value. The study recommends that, school administrators and instructors should identify and remove causes for the students’ performance, which were falling below the lower control limit which indicated a negative shift in performance and implements factors of the students’ performance whom fell above the upper control limit and indicated the positive shift in performance.
Evaluation of toxic metals and radionuclide levels in root vegetables grown in the vicinity of Bahi uranium deposit
(The University of Dodoma, 2022) Ndai, Kelvin Didas
The presence of large uranium deposit in Kisalalo area in Bahi district has raised concerns on the contamination of food groups grown in the vicinity. This study has assessed the levels of concentration of toxic metals including arsenic (As), Cadmium (Cd), Chromium (Cr), Mercury (Hg) and Lead (Pb) and radionuclides including Thorium (232Th), Radium (226Ra) and Potassium (40K) in cassava (Manihot Esculenta) and sweet potatoes (Ipomoea Batatas) from Bahi district.Characterisation of toxic metals and radionuclides was done using Energy Dispersive X-Ray Fluorescence and Gamma Ray Spectrometries respectively. Cassava and sweet potatoes from Bahi ward were found to accumulate higher concentration of toxic metals than in other areas. The highest mean concentration of Cd, Cr, Hg and Pb were found to be 7.91 𝑚𝑔/𝑘𝑔, 34.68 𝑚𝑔/𝑘𝑔, 2.19 𝑚𝑔/𝑘𝑔, and 2.78 𝑚𝑔/ 𝑘𝑔respectively and were approximately 80, 34, 22, and 28 times higher than their respective maximum tolerable limits.Cr levels in cassava and sweet potatoes were highest than other toxic metals due to presence of Cr in the soil and its higher soil to plant transfer factor while As levels were the least almost around tolerable limit.Furthermore, the highest mean activity concentration of 232Th was found to be 9.98 𝐵𝑞/𝑘𝑔in sweet potatoes from Bahi ward while that of 226Ra was 6.63 𝐵𝑞/𝑘𝑔 in sweet potatoes from Bahi ward and that of 40K was 528.43 𝐵𝑞/𝑘𝑔 in cassava from Bahi ward. The highest total annual effective dose due to consumption of cassava and sweet potatoes was found to be 0.0133 mSv/year from Bahi ward but this was within the recommended limit of 1 mSv/year set by FAO/WHO.The results show that cassava and sweet potatoes grown in Bahi ward which is closest to the Kisalalo Uranium deposit site had the highest accumulation of toxic metals.It is thus suggested that the root vegetables are not suitable to be grown in this place as they contribute to exposing consumers to toxicity of heavy metals. On the other hand, despite the presence of the above mentioned radionuclides, the annual effective dose due to consumption of radionuclides is very low and this suggests that the root vegetables do not contribute much in exposing consumers to radiation toxicity.
Existence and uniqueness of the solution to nonlocal problem for a loaded parabolic equation and its numerical approximation
(The University of Dodoma, 2018) Mataru, Bilali
This research presents the existence and uniqueness of a solution to nonlocal problem for a loaded parabolic equation. The nonlocal condition of ﬁrst kind is expressed to its equivalent nonlocal condition of second kind, which is necessary for qualitative study about the solvability of the problem. The theoretical analysis of study on existence and uniqueness of a generalized solution to a nonlocal problem is studied using Galerkin method, apriori method to obtain the approximate size of solution, numbers of inequalities and Gronwall’s lemma. The numerical approximation of the problem is obtained by using homotopy analysis method, where the initial base function is determined by using initial condition.
Finite element method with damping control multi-step methods approach to one boundary value problem for the wave equation.
(The University of Dodoma, 2016) Leandry, Leonce
Over the previous years ﬁnite element method (FEM) has become a powerfully tool to approximate solution of differential equations and prove their existence. The purpose of this research is to introduce and describe a number of the ﬁnite element method (FEM) technique applied to problems for partial differential equations (PDEs) with special attentions to the hyperbolic problems in case of wave and damped wave equations. Another aim is to study the one boundary value problem (BVP) for the wave equation and apply damping control multi-step methods integrated into the FEM such as the Newmark method, Backward difference method (BDF) and Hilber-Hughes-Taylor Method (HHT). The ordinary differential equation (ODE) system obtained after applying FEM are then solved by these multi-step methods, where by the BDF-Method and the HHT-Method are second order precision, unconditionally stable and able to dissipate high-modes for some values of the parameters.
Forecasting membership enrollment of National Health Insurance Fund (NHIF): a case study of Dodoma region
(The University of Dodoma, 2017) Kornelio, Johnas David
The ability to model and perform decision modeling and analysis is an essential feature of many real-world applications. Almost all the decisions in any organization are based on forecasts. Every decision becomes operational at some point in the future, so it should be based on forecasts of future condition. Keeping this in view, an attempt has been made in this dissertation work to study the pattern of NHIF memberships, to select the best model and to forecast the NHIF membership on monthly basis using statistical time series modeling. National Health Insurance Fund membership enrolment forecasting is very essential in the management and providing good and quality health services to the citizen. Majority of decision makings like introduction of programs and infrastructure improvements are easily made with the aid of NHIF membership forecasts. In this dissertation, the NHIF membership enrolment of Dodoma region from 2002 to 2016 has been modeled using Box-Jenkins Autoregressive Integrated Moving Average model technique. The NHIF membership has been further forecasted to the financial year 2016/2017 to 2017/2018 (twenty four months) using seasonal ARIMA(1,2,0)(0,0,1)12 for male, seasonal ARIMA(0,2,0)(1,0,0)12 for female and seasonal ARIMA(0,2,1)(0,0,1)12 for total combined population. The model has been validated using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Ljung-Box statistic values, graphical techniques like time series plots, Q-Q plots and histograms and p-values. The results show that the NHIF membership registration will grow up by the financial year 2016/2017 to 2017/2018 when only time is considered as a factor. The study also explores briefly the recourses required to support current and forecasted NHIF members.
Forecasting of climate variables in Mbeya region
(The University of Dodoma, 2020) Chisunga, Moses
Tanzania, like other countries in the world, is affected by climate change. There is enough evidence to substantiate this that comes from the increase of temperatures across the country over the past thirty years. Despite the mitigations approved to attack the problem of climate change in the country, forecasting of climate variables is a prerequisite. Studies about climate change that have been conducted in Tanzania have mainly focused on assessing the weakness and adaption to the effects of climate change in Tanzania while using either temperature or rainfall variables. Further, the studies have depended on the information at the national level rather than the regional level. To fill this gap, this study forecast the climate variables in Mbeya Region. Specifically, the study analyzed the pattern of climate in Mbeya region with the help of the fit climate model using time series techniques and the fitted model. The climate variables included in the study are temperature, rainfall, evaporation, humidity, and wind speed. The study used secondary data from 1981-2019 collected from Tanzania Meteorological Authority (TMA), Mbeya center. The analysis of the data revealed that the patterns of climate variables are seasonal for monthly data while observing the yearly data trend. Either, there was no data to show irregularities and cyclic components. Basing on the theory of Box and Jenkins, SARIMA were fitted and used to forecast rainfall and temperature respectively. The study recommends Box and Jenkins to be used to get the ARIMA model, either seasonally or non-seasonally.
Forecasting performance of students in mathematics in certificate secondary education examination (CSEE) in Zanzibar
(The University of Dodoma, 2017) Mussa, Asha Moh'd
This study has been conducted with the main objectives to investigate the pattern of students’ performance in mathematics and to forecast the performance of students in mathematics in secondary schools in Zanzibar for next 6 years on the basis of best selected model. The study used secondary data of all 64,446 students from 123 schools of Zanzibar, who sat for final examination from 1986-2016. The yearly data of students' results were collected from Ministry of Education and Vocational Training Zanzibar ( MoEVTZ) and the yearly time series examination result data for CSEE in Zanzibar from 1986-2016 were compiled for Male students , Female students and total students combined in the form of percentage credit, percentage pass and percentage fail. These data were further analyzed for checking and testing of normality. Normality assumption was validated for male students, female students and total students individually by using Kolmogorov-Smirnov test and Shapiro-Wilk’s test. Further, in this study, various Autoregressive Integrated Moving Average (ARIMA) model have been fitted to see the pattern of performance of male students, female students and total students. The best fitted model has been selected on the basis of Akaike Information criterion and Bayesian Information criterion. ACFs and PACFs have also used and the best ARIMA models have been identified as ARIMA (1, 1, 2), ARIMA (2, 1, 0) and ARIMA (1, 1, 0) for male students' percentage credit, percentage pass and percentage fail, ARIMA (1, 1, 1), ARIMA (2, 1, 1) and ARIMA(2, 1, 2) for female students' percentage credit, percentage pass and percentage fail and ARIMA(2, 1, 0), ARIMA (1, 1,2) and ARIMA (1, 1, 0) for total students' percentage credit, percentage pass and percentage fail respectively. Accordingly, the forecast for next six years for all the three cases have been presented.
Fourier transform and the fundamental solutions of mechanical models with internal body forces
(The University of Dodoma, 2015) Carl, Collin Henry
In this dissertation, it is considered, the investigation of the Fourier Transform and the fundamental solutions of mechanical models with internal body forces. Although, there are many models, only two models are considered on the review, namely heat conduction and linear isotropic elasticity. For the investigation, the statement of the problem bases only on the linear isotropic elasticity problem. In working with calculations, the Fourier Transform, Inverse Fourier Transform, Residue Theorem, Jordan‟s Lemma, are applied in particular as well as the complex analysis and integration are applied in general. The obtained results of the statement of the problems having two cases, namely first and second cases, satisfy both their relevant equations and corresponding conditions accordingly. Therefore, they are identified as the fundamental solutions of their corresponding cases according to the problem. In the conclusion, the reviews also show that the Fourier Transform is widely applicable in variety of fields such as electromagnetic fields, magnetic resonance imaging (MRI) and quantum physics. Generally, it is also important in mathematics, engineering, and physical sciences. Finally, the investigator of this writing advises more application of the Fourier Transform since there is a lot of problems which are difficult/nearly impossible to solve directly, become easy after using a Fourier Transform. Also, it is reported that the mathematical operations on functions, like derivatives or convolutions, become much more manageable on the far side of a Fourier Transform.
Generalized exact anisotropic neutral star model with embedding approach
(The University of Dodoma, 2022) Pastory, Makalo
Using embedding approach, this study presents exact solutions to the Einstein field equations for anisotropic neutral stars in more generalized form. The study involves a generalization of the choice of metric potential made by Mathias, Maharaj, Sunzu and Mkenyeleye in which the choice of metric potential is in more specific form. Under embedding approach, one of the metric potentials is chosen on physical grounds while the Karmarkar condition is used to generate the second metric potential. Modelled masses and radii in acceptable ranges for neutral stars are found. Moreover, masses and radii consistent with stars like LMCX-4, Her X-1, cen X-3, 4U 1538-52, vela X-1, and SAX J1808.4-3658 are also generated.
Generalized exact anisotropic neutral star model with embedding approach
(2022) Pastory, Makalo
Using embedding approach, this study presents exact solutions to the Einstein field equations for anisotropic neutral stars in more generalized form. The study involves a generalization of the choice of metric potential made by Mathias, Maharaj, Sunzu and Mkenyeleye in which the choice of metric potential is in more specific form. Under embedding approach, one of the metric potentials is chosen on physical grounds while the Karmarkar condition is used to generate the second metric potential. Modelled masses and radii in acceptable ranges for neutral stars are found. Moreover, masses and radii consistent with stars like LMCX-4, Her X-1, cen X-3, 4U 1538-52, vela X-1, and SAX J1808.4-3658 are also generated.

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