Browsing by Author "Lotsi, A."
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Item Application of Numerical Integration to Stochastic Estimation of the Gini Coefficient(University of Ghana, 2015-07) Darkwah, K.A.; Nortey, E.N.N.; Lotsi, A.; University of Ghana, College of Basic and Applied Sciences School of Physical and Mathematical Sciences Department of StatisticsOver the years, measuring inequality based on the distribution of income has been a major concern to economist. Inequality has had a broader concept than poverty in that it is defined over the entire population not just for the portion of the population below a certain poverty line. The Gini coefficient satisfy many desirable properties of a good measure of inequality such as mean independence, population size independence, symmetry, and Pigou-Dalton Transfer sensitivity. The empirical observation (income) distribution exhibit excess kurtosis and heavy tails. This research first described the probability distribution of income. The study presented a proposed numerical integration method to stochastic estimation of the Gini coefficient. The Proposed Numerical Integration Method showed a better estimate of functions as compared to the Newton’s cotes methods such as the Trapezium rule, Simpson’s 1=3 rule, Simpson’s 3=8 rule, Boole’s rule and Weddle’s rule. Diagnostic tests such as Q-Q plots and Kolmogorov-Smirnov test were graphically and quantitatively used to assess the fitness to the income data respectively. The study therefore concludes that the proposed method is superior to the Newton-Cotes methods of integration. Also, the Gini coefficient estimate using the proposed numerical integration method with k=3 was 0.48 which shows that there is disparity in income in Ghana and recommend to statisticians or mathematicians to use the proposed numerical integration method when computing functions that can’t be easily integrated.Item Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve(SpringerPlus, 2016-07) Darkwah, K.A.; Nortey, E.N.N.; Lotsi, A.The main objective of the study is to compare the Newton–Cotes methods such as the Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the area under the Lorenz curve and Gini coefficient of income using polynomial function with degree 5. Comparing the Gini coefficients of income computed from the Polynomial function with degree 5 for the Trapezium, Simpson 1/3 and Simpson 3/8 methods using the relative errors showed that the trapezium rule, Simpson’s 1/3 rule and Simpson’s 3/8 rule show negative biases with the Simpson 1/3 rule yielding the lowest absolute relative true error of 4.230711 %. © 2016, The Author(s).Item Exact Matrix Completion via Convex Optimization(2016-03-10) Lotsi, A.; Doku-Amponsah, K.We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys for some positive numerical constant C, then with very high probability, most n*n matrices of rank r can be perfectly recovered by solving a simple convex optimization problem. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Our results are connected with the recent literature on compressed sensing, and show that objects other than signals and images can be perfectly reconstructed from very limited information.Item Generalised Bernoulli Model for Correlated Binary Responses: Application to the National Income Dynamics Study (Nids) Datasets(University of Ghana, 2016-06) Fleku, M.; Lotsi, A.; Doku-Amponsah, K.; University of Ghana, College of Basic and Applied Sciences School of Physical and Mathematical Sciences Department of StatisticsThe bivariate Bernoulli model was used to estimate covariate parameters for conditional as well as marginal models for the NIDs datasets. This is a follow- up research on one conducted by Islam et al. (2012) which introduced the use of the bivariate Bernoulli model to properly specify the dependence among bivariate binary responses. The covariate parameters were estimated by first expressing the proposed model in the exponential family form, finding the log-likelihood function and then the corresponding estimating equations. The Newton Rahpson and the Nelder Mead methods of iteration were used to estimate the covariate parameters. The research revealed that the bivariate Bernoulli model fitted bivariate binary response data significantly better than the conditional logistic and the Generalized Estimating Equation (GEE) logistic models-marginal model. The result was same for both artificial and real-life data. It is worth mentioning that to aim at more efficient covariate estimates, the bivariate Bernoulli model is highly recommended for bivariate binary response data. However, further research is needed to choose an initial value when using the Newton Rahpson and the Nelder Mead methods of iteration, because it posed a serious challenge in this study. Again further research is recommended to probably use the multivariate Bernoulli distribution to fit multivariate binary response data and estimate covariate coefficients.Item Joint large deviation principle for some empirical measures of the d-regular random graphs(Taylor & Francis Group, 2021) Ibrahim, U.; Lotsi, A.; Doku-Amponsah, K.In this paper, we define a d–regular random model by perfect matching of vertices or paring of vertices. For each vertex, we assign a q–state spin. From this d–regular graph model, we define the empirical co-operate measure, which enumerates the number of co-operation between a given couple of spins, and empirical spin measure, which enumerates the number of sites having a given spin on the d–regular random graph model. For these empirical measures, we obtain large deviation principle(LDP) in the weak topology.Item Longevity risk—Its financial impact on pensions(Scientific African, 2022) Nantwi, N.P.A.; Lotsi, A.; Debrah, G.We study the financial impact of longevity risk on defined benefit (DB) pension plan liabilities using the 2010 Ghana population census, and the Lee-Carter model. We compare the usual Lee-Carter model to an extended version. While we observe that Ghana’s mortality has decreased, our results show that longevity risk raises the cost of liability. We propose that defined benefit scheme trustees and fund managers, assess their funds and act on the assets available to them in a Liability-Driven Investment (LDI) Strategy tailored to the dynamics of their scheme - since there is no single best method in LDI strategy. This study may help policymakers or practitioners in their efforts to mitigate the effects of longevity risk.Item Modeling Gdp Using Vector Autoregressive (Var) Models: An Empirical Evidence from Ghana.(University of Ghana, 2015-06) Amoah, E.; Baidoo, I. K.; Lotsi, A.; University of Ghana, College of Basic and Applied Sciences, School of Physical and Mathematical Sciences, Department of StatisticsThis study used the VAR models to model the Growth Domestics Products (GDP) of Ghana with other two selected macroeconomic such as inflation and real exchange rate for the period of 1980 to 2013. Data were taken from the World Bank’s World Development Indicators and Bank of Ghana. This study employed co-integration test and vector error correction models (VECM) to examine both long-run and short-run dynamic relationships between the GDP and the macroeconomic variables. The time series properties of the data were, first, analysed using the Augmented Dickey-Fuller (ADF) test. The empirical results derived indicate that all the variables were stationary after their first differencing; i.e. variables are integrated of order one, I(1). The study further established that there is cointegration between macroeconomic variables and GDP in Ghana indicating long run relationship. The VECM (3) model was appropriately identified using AIC information criteria with co-integration relation of exactly one .The above long term relation indicates that Real Exchange Rate have a negative effect on GDP whiles Inflation (CPI) showed a positive effect on GDP. The study further investigated the causal relationship using the Granger Causality analysis, which indicates a uni–directional causal relationship between GDP and Real Exchange rate and bi-directional causal relationship between GDP and Inflation rate at 5%. Hence the findings that inflation has a long-run relationship between GDP growth and influences it positively in Ghana, government should invest in local industries to boost domestic production of tradable which would maintain higher export volumes. This will help reduce Exchange rate and hence impact on inflation, thereby increasing GDP growth rate.Item Modeling Maternal Mortality in Ghana Using Hierarchical Models (2010-2013)(University of Ghana, 2015-06) Tawiah, K.; Lotsi, A.; Iddi, S.; University of Ghana, College of Basic and Applied Sciences, School of Physical and Mathematical Sciences, Department of StatisticsThis thesis examined the appropriate model that best fit maternal mortality data in fifty six health facilities in the Central, Eastern, Greater Accra and Western regions of Ghana from 2010 to 2013 as well as factors contributing to this menace in the various health facilities. The study began with the application of a simple Poisson regression model which was extended to capture the hierarchical structure, overdispersion and zero-inflation. Expressions for the mean, variance and score equations were derived. All estimations were done in the maximum likelihood framework. In this thesis we show that all different extensions of the Poisson model is based on mixture of distributions. The overall best model showed that maternal mortality in the various health facilities in Ghana depends on the number of referrals (into and out of hospital facility), number of antenatal visits exceeding four, number of obstetric cases with HIV/AIDS, number of obstetric cases with malaria, number of medical doctors and number of midwives at the facility. We found that maternal mortality was significant in all four regions and for all years considered and that more pregnant women attend antenatal at clinics (Polyclinics, clinics, health centers and community health planning service centers) than in hospitals (general hospitals, regional hospitals and teaching hospitals) but more of them deliver in the hospitals than in the clinics. 2.3% and 12.9% of the pregnant women had HIV/AIDS and malaria respectively. Eclampsia and Pre-Eclampsia were the leading direct cause of maternal death while anaemia in pregnancy was second to a collection of other complications for the indirect cause. Finally, we estimated Ghana‟s maternal mortality ratio at 382 per 100000 live births. Key words: Poisson regression model, hierarchical models, overdispersion, maternal mortality ratio, zero-inflated models.Item Portfolio Optimization Using Minimum Variance Line Approach: A Case Study of the Social Security and National Insurance Trust(Ghana Social Science Journal, 2017-12) Nkum, N.; Lotsi, A.; Chapman-Wardy, C.; Doku-Amponsah, K.The main motive of investors around the globe is to invest in assets with the idea of maximizing the return with a minimum risk of investment. The management of investment portfolio requires carefully selecting various assets to invest in, as well as managing the proportions of funds to be channeled into a particular investment. The data used in this study was obtained from Social Security and National Investment Trust (SSNIT) covering a five-year period spanning from 2010 to 2014. The data comprised of the prices of Investment Properties (IVP), Investment to Maturity (IVM) and Loans Receivable (LR), out of which the expected return of each asset, the standard deviation (SD) of each asset, the correlation between assets and the covariance between assets are computed. The methodology used here was the minimum variance line approach proposed by Harry Markowitz. The model allowed us to assign weights to various investment classes by transposing the expected returns and risk associated with them. The result showed that, as the expected return of the portfolio increases the various percentage weight to be invested in IVP and LR increase whilst that of IVM decreases. The portfolio standard deviation or risk on the other hand also increases with increasing portfolio expected returnsItem Statistical Analysis of Public Sentiment on the Ghanaian Government: A Machine Learning Approach(Hindawi, 2021) Andoh, J.; Asiedu, L.; Lotsi, A.; Chapman-Wardy, C.Gathering public opinions on the Internet and Internet-based applications like Twitter has become popular in recent times, as it provides decision-makers with uncensored public views on products, government policies, and programs. Through natural language processing and machine learning techniques, unstructured data forms from these sources can be analyzed using traditional statistical learning. The challenge encountered in machine learning method-based sentiment classification still remains the abundant amount of data available, which makes it difficult to train the learning algorithms in feasible time. This eventually degrades the classification accuracy of the algorithms. From this assertion, the effect of training data sizes in classification tasks cannot be overemphasized. This study statistically assessed the performance of Naive Bayes, support vector machine (SVM), and random forest algorithms on sentiment text classification task. The research also investigated the optimal conditions such as varying data sizes, trees, and kernel types under which each of the respective algorithms performed best. The study collected Twitter data from Ghanaian users which contained sentiments about the Ghanaian Government. The data was preprocessed, manually labeled by the researcher, and then trained using the aforementioned algorithms. These algorithms are three of the most popular learning algorithms which have had lots of success in diverse fields. 'e Naive Bayes classifier was adjudged the best algorithm for the task as it outperformed the other two machine learning algorithms with an accuracy of 99%, F1 score of 86.51%, and Matthews correlation coefficient of 0.9906. The algorithm also performed well with increasing data sizes. 'e Naive Bayes classifier is recommended as viable for sentiment text classification, especially for text classification systems which work with Big Data.Item Survival Pattern of First Accident among Commercial Drivers in the Greater Accra Region of Ghana(Accident Analysis and Prevention, 2017-06) Nanga, S.; Odai, N.A.; Lotsi, A.In this study, the average accident risk of commercial drivers in the Greater Accra region of Ghana and its associated risks were examined based on a survey data collected using paper-based questionnaires from 204 commercial drivers from the Greater Accra Region of Ghana. The Cox Proportional Hazards Model was used for multivariate analysis while the Kaplan-Meier (KM) Model was used to study the survival patterns of the commercial drivers. The study revealed that the median survival time for an accident to happen is 2.50 years. Good roads provided a better chance of survival than bad roads and experienced drivers have a better chance of survival than the inexperienced drivers. Age of driver, alcohol usage of driver, marital status, condition of road and duration of driver's license were found to be related to the risk of accident.Item Time Series Modelling for Total Number of Defective Parts of Printed Circuit Boards in the Manufacturing Industry in Ghana(University of Ghana, 2015-07) Maha, Y.S.; Lotsi, A.; Mettle, F.O.; University of Ghana, College of Basic and Applied Sciences, School of Physical and Mathematical, Sciences Department of StatisticsFor stochastic time series modelling, an essential property is the underlying statistical model that is assumed to govern the number of defective parts of printed circuit boards in a production process in the manufacturing industries in Ghana. The data was for a period spanning from 2009 to 2014. Considering time series methodology, we specify differences in the data points as a stochastic process assumed to have Markov dependency with respective state transition probabilities matrices following the identified state space (i.e. increase, decrease or remain the same). We observed that the identified states communicate, hence the chains are aperiodic and ergodic signifying the possessing of limiting distributions. We established a methodology for determining wthether the daily number of defective parts increase, decrease or remained the same. A criteria for identifying the state(s) in which production of printed circuit boards is cost effective based on least transition probabilities was also applied. The established methodology is applied to daily number of defective parts during printed circuit boards production in the manufacturing industries in Ghana. Chapman-Kolmogorov Equations and time series models were used in this study.The results showed that it was cost effective when productions are done in the first and second states since at these states least number of defective parts of printed circuit boards is recorded.The n-step probabilities were also determined by subjecting the transition matrix to powers.Autoregressive and moving average method was also applied. The data was differenced once for stationarity which was confirmed by the Augmented Dickey-Fuller Test. The model that was adjudged the best was the model with least AIC and BIC values. ARMA (1,1) model was adjudged the most ideal model for forecasting in this study since it met all the requirements of an ideal model.