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Modeling Extremal Events: A Case Study of the Kenyan Public Debt
Josephat Onchangwa Motonu,
Anthony Gichuhi Waititu,
Joseph Kyalo Mung’atu
Issue:
Volume 5, Issue 6, November 2016
Pages:
334-341
Received:
14 September 2016
Accepted:
23 September 2016
Published:
14 October 2016
Abstract: Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the recent surge in mega infrastructure development which is anticipated to continue triggering uptake, and piling of more public debt. To model this phenomenon, this study has applied the Extreme Value Theory in modeling the public debt where Generalized Pareto Distribution has been used and subsequently, Value-at-Risk determined. Generally, the differenced debt stock data has been modeled by fitting the Generalized Pareto Distribution and a debt sustainability threshold has been determined as 1.263. This is interpreted to imply that the prevailing year's borrowing should not occasion a rise in public debt beyond 26.3 per cent of the previous year's level. Specifically, both the unconditional and conditional Value-at-Risk has been ascertained as 1.263 and 0.957 respectively, at α = 0.05 level of significance, which is the maximum tolerable debt limit. Further, by applying the loss function, it has been established that among the two methods, conditional Value-at-Risk is the efficient model for measuring public debt risk, connoting that at α = 0.05, the current year's borrowing, say, should occasion a public debt reduction by 4.27 per cent from the previous one for the country to vacillate within the debt sustainability realms. Finally, it is recommended that a further study be conducted by computing and using Net Present Value of debt indicators since the ones used in this study are aggregated in nominal terms.
Abstract: Kenya’s public debt is sharply increasing and there are fears that in the long run, the situation in the country may, perhaps, be gravitating towards the boundaries of debt distress. This has been occasioned by the ever rising fiscal deficit as a result of high expenditure appetite and poor performance of tax revenue. In addition to that is the rec...
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Empirical Bayes One-side Test for Inverse Exponential Model based on Negative Associate Samples
Issue:
Volume 5, Issue 6, November 2016
Pages:
342-347
Received:
5 September 2016
Accepted:
23 September 2016
Published:
15 October 2016
Abstract: By using the kernel-type density estimation and empirical distribution function in the case of identically distributed and negatively associated samples, the empirical Bayes one-sided test rules for the parameter of inverse exponential distribution are constructed based on negative associate sample under weighted linear loss function, and the asymptotically optimal property is obtained . It is shown that the convergence rates of the proposed empirical Bayes test rules can arbitrarily close to O(n-1/2) under suitable conditions.
Abstract: By using the kernel-type density estimation and empirical distribution function in the case of identically distributed and negatively associated samples, the empirical Bayes one-sided test rules for the parameter of inverse exponential distribution are constructed based on negative associate sample under weighted linear loss function, and the asymp...
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Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values
Issue:
Volume 5, Issue 6, November 2016
Pages:
348-353
Received:
21 September 2016
Accepted:
1 October 2016
Published:
25 October 2016
Abstract: The aim of this paper is to study the estimation of parameter of Burr Type XI distribution on the basis of lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes and empirical Bayes estimators of the unknown parameter are derived under entropy loss function. Finally, the admissibility and inadmissibility of a class of inverse linear estimators are discussed.
Abstract: The aim of this paper is to study the estimation of parameter of Burr Type XI distribution on the basis of lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes and empirical Bayes estimators of the unknown parameter are derived under entropy loss function. Finally, the adm...
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Multiple Local Polynomial Regression Modelling: Case of Life Insurance Uptake in Kenya, Uasin Gishu County
Willy Thuitai,
Anthony Gichuhi Waititu,
Anthony Wanjoya
Issue:
Volume 5, Issue 6, November 2016
Pages:
354-358
Received:
26 September 2016
Accepted:
5 October 2016
Published:
27 October 2016
Abstract: In Kenya life insurance has contributed widely and still remains a vital aspect of the social-economic development of the society. It focuses on safe- guarding the future as well as ensuring that there is some savings that can be used later in life. Despite its importance, the penetration of life insurance is currently only at one point three percent in Kenya. This is a small percentage in comparison to the developed countries where life insurance penetration is quite high. In this research, local regression (LOESS) method was used. LOESS specifically denotes a method that is also known as locally weighted polynomial regression. At each point in the data set a low-degree polynomial is fitted to a subset of the data, with explanatory variable values near the point whose response is being estimated. In local polynomial regression, a low-order weighted least squares(WLS) regression is fit at each point of interest using data from some neighbourhood around x. The value of the regression function for the point is then obtained by evaluating the local polynomial using the explanatory variable values for that data point. In this research income, education, age and marital status were found as the major factors associated with low insurance intake in Uasin Gishu County. The research highly recommends the insurance companies to apply the knowledge of LOESS to determine the major factors associated with low life insurance uptake in the country. Insurance companies should strive to provide educative seminars to the public to increase life insurance uptake. In this research we had uptake of life insurance as dependent variable and level of income, education level, age and marital status being independent variables.
Abstract: In Kenya life insurance has contributed widely and still remains a vital aspect of the social-economic development of the society. It focuses on safe- guarding the future as well as ensuring that there is some savings that can be used later in life. Despite its importance, the penetration of life insurance is currently only at one point three perce...
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Sarima Versus Time Lagged Feedforward Neural Networks in Forecasting Precipitation
Elias Kimani Karuiru,
George Otieno Orwa,
John Mwaniki Kihoro
Issue:
Volume 5, Issue 6, November 2016
Pages:
359-364
Received:
17 September 2016
Accepted:
17 October 2016
Published:
7 November 2016
Abstract: The precipitation estimates are considered to be very important in economic planning. Major economic sectors highly depend on the precipitation levels. These sectors include agriculture, tourism, mining and transport. In Kenya, rainfall amount fluctuates with time hence depending on empirical observations while predicting is a hard task. Various statistical techniques have been used in forecasting precipitation. Among these techniques is Holt Winters procedures and SARIMA due to the seasonality effect. SARIMA model has been found to be effective in forecasting precipitation. The model has therefore been the most commonly used while precipitation forecasts are required. However, there is no any statistical research that has been carried out to test the effectiveness of neural networks in forecasting precipitation. This research hence considered forecasting precipitation using SARIMA and TLFN models. Box-Jenkins procedures of forecasting were used. Comparison of forecasts from the two techniques was done through the use of Mean Absolute Deviation (MAD), Mean Squared Deviation (MSD) and Mean Absolute Percentage Error (MAPE) in order to conclude which technique gives the better forecasts. Time Lagged Feed forward Neural Network model performed better than Seasonal Autoregressive Integrated Moving Average.
Abstract: The precipitation estimates are considered to be very important in economic planning. Major economic sectors highly depend on the precipitation levels. These sectors include agriculture, tourism, mining and transport. In Kenya, rainfall amount fluctuates with time hence depending on empirical observations while predicting is a hard task. Various st...
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Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution
Thuto Mothupi,
Wilson Moseki Thupeng,
Baitshephi Mashabe,
Botho Mokoto
Issue:
Volume 5, Issue 6, November 2016
Pages:
365-375
Received:
10 October 2016
Accepted:
22 October 2016
Published:
14 November 2016
Abstract: In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.
Abstract: In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme ...
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A New Non-parametric Test Procedure for the Median of an Asymmetrical Population
Mohammad Ibrahim Ahmmad Soliman Gaafar
Issue:
Volume 5, Issue 6, November 2016
Pages:
376-386
Received:
11 October 2016
Accepted:
25 October 2016
Published:
17 November 2016
Abstract: This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.
Abstract: This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed m...
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A Screening Experiment on a Diabetes Mellitus Herbal Formulation
Gladys Gakenia Njoroge,
Joseph Arap Koske,
Jemimah Ayuma Simbauni
Issue:
Volume 5, Issue 6, November 2016
Pages:
387-394
Received:
15 October 2016
Accepted:
27 October 2016
Published:
18 November 2016
Abstract: Screening experiments are usually performed on mixtures in order to determine the experimental variables that have significant influence on the targeted response. In this study, a screening experiment was carried out on a herbal formulation prescribed by a registered Kenyan herbalist to diabetes mellitus type II patients. The herbal formulation was composed of the following six herbs: Utica dioica, Moringaoleifera, Cinnamomum verum, Azadirachta indica, Momordica charantia and Gymnema sylvestre. The targeted response was the change that had occurred in blood glucose level 2 hours after the herbal drug treatment had been administered to alloxan induced diabetic albino wistar rats. An axial mixture design with replicated centre points was adopted and a first degree mixture model fitted to the data. The axial mixture design was constructed using Design Expert® software with randomly distributed 23 design points positioned on the component axes. The analysis of the data was carried out using the R statistical software environment. The results showed that Cinnamomum verum and Azadirachta indica caused the highest change individually on the blood glucose level among the six herbs. The complete mixture of the six herbs registered the lowest reduction in the blood glucose level. We recommend that the two herbs, Cinnamomum verum and Azadirachta indica, be tested farther to find out the most optimal conditions for their extraction in terms of temperature and time so as to produce a maximum reduction on the blood glucose level. In addition, we recommend that this study be extended to higher animals to establish whether the same patterns would be observed and also obtain the appropriate dosage levels.
Abstract: Screening experiments are usually performed on mixtures in order to determine the experimental variables that have significant influence on the targeted response. In this study, a screening experiment was carried out on a herbal formulation prescribed by a registered Kenyan herbalist to diabetes mellitus type II patients. The herbal formulation was...
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