Browsing by Author "Garba, M. K."
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Item Compact Fluorescent Lamps and Electricity Consumption Trend in Residential Building in Ilorin, Nigeria(International Journal of Energy Sector Management, 2011-06-21) Sule, B. F.; Ajao, K. R.; Ajimotojan, H. A.; Garba, M. K.Purpose – The purpose of this study is to examine the electricity consumption trend in residential buildings using incandescent lamps and retrofitting with compact fluorescent lamps (CFLs). Design/methodology/approach – Questionnaires were administered to capture the necessary data from three randomly selected residential estates in Ilorin, Nigeria. In total, 8,840 sampled incandescent lamps were retrofitted with CFLs. The electric energy in kilowatt hour (kWh) consumed prior to replacement for three months was compared with kWh consumption after retrofitting and analyzed employing t-tests. Findings – The three-month average electricity consumption of ten households for the University of Ilorin GRA quarters and Lower Niger River Basin staff quarters pre- and post-installation were 20,259 and 13,010 kWh, and 46,891 and 29,588 kWh, respectively. Results show that there were significant differences between the observed and tabulated values for the pre- and post-installation of CFLs, respectively, at 5 per cent confidence level. About 40 per cent reduction in electricity consumption was achieved through deployment of CFLs in the residential households. Originality/value – This paper demonstrates how retrofitting of incandescent lamps with CFLs can bring about possible reduction in electricity consumption in residential households in Nigeria.Item Efficient Support Vector Machine Classification of Diffuse Large B-Cell Lymphoma and Follicular Lymphoma mRNA Tissue Samples(Annals Computer Science Series, 2015-04-25) Banjoko, A. W.; Yahya, W. B.; Garba, M. K.; Olaniran, O. R.; Dauda, K. A.; Olorede, K. O.This paper proposes a weighted Support Vector Machine (w-SVM) method for efficient class prediction in binary response data sets. The proposed method was obtained by introducing weights which utilizes the point biserial correlation between each of the predictors and the dichotomized response variable into the standard SVM algorithm to maximize the classification accuracy. The optimal value of the proposed w-SVM cost and each of the kernels parameters were determined by grid search in a 10-fold cross validation resampling method. Monte-Carlo Cross Validation method was employed to examine the predictive power of the proposed method by partitioning the data into train and test samples using different sampling splitting ratios. Application of the proposed method on the simulated data sets yielded high prediction accuracy on the test sample. Results from other performance indices further gave credence to the efficiency of the proposed method. The performance of the proposed method was compared with three of the state-of-the art machine learning methods including the standard SVM and the result showed the superiority of this method over others. Finally, the results generally show that the modified algorithm with Radial Basis Function (RBF) Kernel perform excellently and achieved the best predictive performance than any of the existing classifiers considered.Item IMPROVED BAYESIAN FEATURE SELECTION AND CLASSIFICATION METHODS USING BOOTSTRAP PRIOR TECHNIQUES(Faculty of Computer and Applied Computer Science, Tibiscus University of Timisoara, Romania, 2016) Olaniran, O. R.; Olaniran, S. F.; Yahya, W. B.; Banjoko, A. W.; Garba, M. K.; Amusa, L. B.; Gatta, N. F.In this paper, the behavior of feature selection algorithms using the traditional t-test, Bayesian t-test using MCMC and Bayesian two-sample test using proposed bootstrap prior technique were determined. In addition, we considered some frequentist classification methods like k- Nearest Neighbor (k-NN), Logistic Discriminant (LD), Linear discriminant analysis (LDA), Quadratic discriminant analysis (QDA) and Naïve Bayes when conditional independence assumption is violated. Two new Bayesian classifiers (B-LDA and B-QDA) were developed within the frame work of LDA and QDA using the bootstrap prior technique. The model parameters were estimated using Bayesian approach via the posterior distribution that involves normalizing the prior for the attributes and the likelihood from the sample in a MonteCarlo experiment. The bootstrap prior technique was incorporated into the Normal-Inverse-Wishart natural conjugate prior for the parameters of the multivariate normal distribution where the scale and location parameters were required. All the classifiers were implemented on the simulated data at 90:10 training-test data ratio. The efficiencies of these classifiers were assessed using the misclassification error rate, sensitivity, specificity, positive predictive value, negative predictive value and area under the ROC curve. Results from various analyses established the supremacy of the proposed Bayes classifiers (B-LDA and B-QDA) over the existing frequentists and Naïve Bayes classification methods considered. All these methods including the proposed one were implemented on a published binary response microarray data set to validate the results from the simulation studyItem Improved Bayesian Feature Selection and Classification Methods Using Bootstrap Prior Techniques(Faculty of Computer and Applied Computer Science, Tibiscus University of Timisoara, Romania, 2016) Olaniran, O. R.; Olaniran, S. F.; Yahya, W. B.; Banjoko, A. W.; Garba, M. K.; Amusa, L. B.; Gatta, N. F.In this paper, the behavior of feature selection algorithms using the traditional t-test, Bayesian t-test using MCMC and Bayesian two-sample test using proposed bootstrap prior technique were determined. In addition, we considered some frequentist classification methods like k- Nearest Neighbor (k-NN), Logistic Discriminant (LD), Linear discriminant analysis (LDA), Quadratic discriminant analysis (QDA) and Naïve Bayes when conditional independence assumption is violated. Two new Bayesian classifiers (B-LDA and B-QDA) were developed within the frame work of LDA and QDA using the bootstrap prior technique. The model parameters were estimated using Bayesian approach via the posterior distribution that involves normalizing the prior for the attributes and the likelihood from the sample in a MonteCarlo experiment. The bootstrap prior technique was incorporated into the Normal-Inverse-Wishart natural conjugate prior for the parameters of the multivariate normal distribution where the scale and location parameters were required. All the classifiers were implemented on the simulated data at 90:10 training-test data ratio. The efficiencies of these classifiers were assessed using the misclassification error rate, sensitivity, specificity, positive predictive value, negative predictive value and area under the ROC curve. Results from various analyses established the supremacy of the proposed Bayes classifiers (B-LDA and B-QDA) over the existing frequentists and Naïve Bayes classification methods considered. All these methods including the proposed one were implemented on a published binary response microarray data set to validate the results from the simulation studyItem Micronumerosity in Classical Linear Regression(College of Natural and Applied Sciences, University of Port Harcourt, Nigeria, 2015) Oyeyemi, G. M.; Bolakale, A; Folorunsho, A. I.; Garba, M. K.This study studied the problem of micronumerosity in Classical Linear Regression (CLR) in other to prescribe appropriate remedy to the problem if encountered at any CLR analysis. The study is aimed at determining an optimum sample size n*, such that when the number of observations of variables in CLR is greater than (i.e n > n*) then micronemerosity is not a problem. It also suggests means of correcting micronumerosity in CLR. The minimum sample size (n) for a given number of independent variables (p) and level of correlation between the dependent and independent variable(s) were determined. Also, Factor analysis served as the best method of overcoming problem of micronumerosity.Item Modeling Effects of some Factors that Contribute to Cereals Yields in Nigeria using Toda-Yamamoto Techniques.(SLU Journal of Science and Technology (SLUJST). Published by the Faculty of Natural and Applied Sciences, Sule Lamido University, Kafin-Hausa, Jigawa State, 2020-03-20) Garba, M. K.; Akanni, S. B.; Yahya, W. B.; Kareem, K. Y.; Afolayan, R. B.In this study, we employed the techniques of Toda-Yamamoto causality test to determine the direction of causality among Cereals Production (CP), Land used for Cereals Production (LP) and Cereal Yields (CY) in Nigeria for the period of 50 years (1966 to 2016).The maximum order of integration and optimal lag order of the series confirmed that VAR (2+1) model best fitted the data. Results from the fitted model estimates revealed that two year past values t-2 (2014 and 2015) of CP is the major determinant of CP series in current time period t (2016) while one year past value t-1 (2015) of CY and two year past values t-2 (2014 and 2015) of CP and LP are major determinants of CY series in current time period t (2016).The results of Toda-Yamamoto causality test showed that CY is Granger-caused by both CP and LP.Item Modeling Nigerian Electricity Generation and Consumption Pattern(Faculty of Sciences, Federal University of Technology Minna, Nigeria, 2015) Garba, M. K.; Ajao, K. R.; Yahya, W. B.; Oyeyemi, G. M.This study examined annual amount of electricity generated and consumed in Nigeria for the period spanning 1970 to 2012. The Box-Jenkins modeling approach was employed after the series were transformed to ensure stationarity using the first differencing method. The empirical results showed that ARIMA (1, 1, 0) and ARIMA (0, 1, 1) models fitted the electricity generation and consumption adequately. The whiteness of the residuals from the model was verified using Ljung-Box methodology. The projections for both electricity generation and consumption for five years ahead were made 80% and 95% confidence limits.Item Multiclass Feature Selection and Classification with Support Vector Machine in Genomic Study(Edited Conference Proceedings of the 1st International Conference of the Nigeria Statistical Society (NSS)., 2017) Banjoko, A. W.; Yahya, W. B.; Garba, M. K.; Olaniran, O. R.; Amusa, L. B.; Gatta, N. F.; Dauda, K. A.; Olorede, K. O.This study proposes an efficient Support Vector Machine (SVM) algorithm for feature selection and classification of multiclass response group in high dimensional (microarray) data. The Feature selection stage of the algorithm employed the F-statistic of the ANOVA–like testing scheme at some chosen family-wise-error-rate (FWER) to control for the detection of some false positive features. In a 10-fold cross validation, the hyper-parameters of the SVM were tuned to determine the appropriate kernel using one-versus-all approach. The entire simulated dataset was randomly partitioned into 95% training and 5% test sets with the SVM classifier built on the training sets while its prediction accuracy on the response class was assessed on the test sets over 1000 Monte-Carlo cross-validation (MCCV) runs. The classification results of the proposed classifier were assessed using the Misclassification Error Rates (MERs) and other performance indices. Results from the Monte-Carlo study showed that the proposed SVM classifier was quite efficient by yielding high prediction accuracy of the response groups with fewer differentially expressed features than when all the features were employed for classification. The performance of this new method on some published cancer data sets shall be examined vis-à-vis other state-of-the-earth machine learning methods in future works.Item Multivariate Time Series Analysis on the Prices of Staple Foodstuffs in Kwara State, Nigeria(Journal of Science, Technology and Mathematics Education (JOSTMED), Federal University of Technology, Minna, 2016-12-15) Afolayan, R. B.; Yahya, W. B.; Garba, M. K.; Adenuga, A. A.; Olatayo, T. O.Due to supplementary, complementary and substitute relationship between staple foodstuffs, the prices of one or more staple foodstuffs tend to influence and could be used to predict the prices of some others. This study was therefore aimed at establishing the co-movement between the prices of some major stable foodstuffs - Rice, Maize, Garri, Millet, Guinea-Corn and Beans - in Kwara State, Nigeria. Multivariate time series models were fitted to data on monthly prices of Rice, Maize, Garri, Millet, Guinea-Corn and Beans over a period of twelve years (from January 2000 to December 2012). The cointegration relations among the prices were established by applying Johansen’s cointegration tests. As a result, appropriate Vector Error Correction (VEC) model was fitted to the data. The unit root test for stationarity in the series reveals that all the series were non-stationary but they were only made to be stationary at first difference. The results from the analysis showed that there exist short term adjustments and long-term dynamics among the prices of Rice, Maize, Garri, Millet, Guinea-Corn and Beans in Nigeria over the study period. Further results showed that a Vector Error Correction (VEC) model of lag two with one cointegration equation best fits the data. The forecasting accuracy of the fitted model was determined by out-of-sample forecasts of the future prices of the selected staple foodstuffs. Suitable model’s assessment criteria such as root mean square error, mean absolute error and the like were employed to determine the efficiency of the fitted model. The data employed for the study were collected from the Kwara State office of National Bureau of Statistics, Nigeria. All analyses were performed in the environment of R Statistical package.Item Multivariate Time Series Modeling of Malaria Incidence in Gombe, Nigeria(Nigerian Association of Mathematical Physics, 2016-11-10) Yahya, W. B.; Mohammed, M. B.; Garba, M. K.Item On the Approximation of Pareto Distribution to Exponential Distribution Using the Gini Coefficient of Inequality(Edited Conference Proceedings of the 1st International Conference of the Nigeria Statistical Society (NSS)., 2017) Yahya, W. B.; Garba, M. K.; Amidu, L.; Olorede, K. O.; Gatta, N. F.; Amusa, L. B.Pareto proposed that income and wealth distribution obeys a universal power law valid for all times and countries, but subsequent studies have often disputed this position. Some even argued there is indeed no Pareto Law and that it should be entirely discarded in studies on distribution of wealth or resources. Many other probability distributions have been proposed such as log normal, exponential, gamma and two other forms by Pareto himself. Using data on imported goods from the National Bureau of Statistics as a case of distribution of wealth in Nigeria, we demonstrated that the distribution of money spent on importation in Nigeria also follow exponential distribution using the Gini coefficient which is a measure of inequality (degree of concentration) of a variable in the distribution of resources. Simulation studies were carried out at different sizes of items (or households) and varying values of the shape parameter and we compare how close the Gini coefficients of the exponential distribution approximate those obtained from the Pareto data as a credible alternative to Pareto distribution.Item On the Strength of Agreement Between Students’ Initial and Final Academic Performances in Nigeria University System.(ABACUS, Mathematical Association of Nigeria, Nigeria, 2018) Banjoko, A. W.; Yahya, W. B.; Abiodun, H. S.; Adeleke, M. O; Afolayan, R. B; Garba, M. K.; Olorede, K. O.; Dauda, K. A.This paper examines the strength of agreement between academic performances of students after their first and final years in the University. Academic performances of a total of 886 students that were admitted into various academic programs in the Faculty of Science, University of Ilorin, during the 2008/2009 academic session were followed-up to their year of graduation in 2012. Information on the grade point average (GPA) of students at the end of their first year in 2008, their final cumulative grade point average (CGPA) at the end of their studies in 2012 among others were collected. Results from this study generally showed a fair agreement between students’ initial and final academic performances in Nigeria University system (p < 0.001). It was also found that about 50% of students maintained the classes of degrees they had in their first year till graduation, about 40% of them improved on their performances while the performances of about 7% of them dropped from what they had during their first year. Further results showed that students’ performance is gender sensitive. Specifically, about 45% and 60% of female and male students maintained the classes of degrees they had during their first year in the University, about 50% and 30% of them improved on theirs while about 5% and 10% of them dropped from their initial academic performances at the end of their studies respectively. Finally, students in the Biological Sciences improved on their initial academic performances more than their counterparts in the Physical Sciences. Also, female students improved on their initial academic performances more than their male counterparts. This work will serve as a useful counselling guide to prospective admission seekers into the Universities and all the stakeholders at enhancing students’ academic performances in the University system.Item Performance Evaluation of Some Estimators of Linear Models with Collinearity and Non–Gaussian Error(Edited Conference Proceedings of the 1st International Conference of the Nigeria Statistical Society (NSS)., 2017) Yahya, W. B.; Garba, M. K.; Ajayi, A. G.; Dauda, K. A.; Olaniran, O. R.; Gatta, N. F.Among typical challenges in numerous multiple linear regression models are those of multicollinearity and non–normal disturbances which have created undesirable consequences for the ordinary least squares (OLS) estimator which is the popular and naïve technique for estimating linear models. Thus, it appears so critical to combine strategies for estimating regression models in order to muddle through while these challenges are present. In this study, the strength of some methods of estimating classical linear regression model in the presence of multicollinearity and non-normal error structures were investigated. The conventional Least Squares (LS), Ridge Regression (RR), Weighted Ridge (WR), Robust M-estimation (M) and Robust Ridge Regression (RRR) methods taking into accounts M-estimation procedures were considered in this study. Results from Monte-Carlo study revealed the superiority of the RRR estimator over others using Mean Squared Errors (MSE) of parameter estimates and Absolute Bias (AB) as assessment criteria among others over various considerations for the distribution of the disturbance term and levels of multicollinearity. The study concluded that whenever linear regression modeling is intended and multicollinearity among the regressors and non-spherical disturbance structure on the response variable are suspected in a data set, the RRR estimator should be adopted in order to ensure optimal efficiency.Item Power Analysis of the Likelihood Ratio Test for Exponential Populations(Transactions of the Nigerian Association of Mathematical Physics (Trans. of NAMP), 2017-05-31) Yahya, W. B.; Kolade, E. I.; Garba, M. K.; Usman, A.The statistical power of the likelihood ratio (LR) test for testing the parameter (λ) of the exponential distribution under different parameter considerations and sample sizes was investigated. Results from Monte Carlo studies showed that the power of the test is highly sensitive to the size of λ_0∈λ under H0 and λ_1∈λ under H1 from the parameter space λ being tested. As the values of both λ_0 and λ_1 progressively increase, more samples would be required before a small shift between them could be detected with appreciable power, even with equal effect sizes |λ_0-λ_1 | over various sizes of λ_0 and λ_1. However, the sample size required to attain a reasonable power by the test reduces as the value of the parameter ratio λ_0/λ_1 decreases with λ_0<λ_1. Further results indicated that fewer samples would be required by the test to achieve appreciable power as the chosen size α level increases. Empirical illustrations are provided to validate the results from Monte Carlo experiments.Item Probabilistic Analysis of Peak Daily Rainfall for Prediction Purposes in Selected Areas of Northern Nigeria(Nigerian Journal of Technological Research (NJTR), Federal University of Technology, Minna, 2016-06-05) Salami, A. W.; Aremu, A. S.; Ayanshola, A. M.; Abdulkadir, T. S.; Garba, M. K.In this study, probability analysis was performed on peak daily rainfall data in order to predict rainfall interval values and to determine the best fit functions in some parts of Nigeria. The selected towns are Kaduna, Kano, Yola, Jos, Damaturu and Maiduguri. The obtained peak daily rainfall values were subjected to Gumbel, Log-Gumbel, Normal, Log-Normal, Pearson and Log-Pearson probability distributions. Mathematical equation for probability distribution functions were established for each town and used to predict peak rainfall. The predicted values were subjected to goodness of fit tests such as Chi-square, Correlation Coefficient, Coefficient of Determination and Errors of Estimates to determine how best the fits are. The model that satisfies the tests adequately was selected as the best fit model. The study revealed that the peak rainfall at Kaduna, Jos, Kano, Yola and Damaturu are best fitted by log-Gumbel, while log- Pearson distribution is suitable for predicting peak rainfall in Maiduguri. The result also shows that the occurrences of peak daily rainfall depth of 100 mm and above are rare in the selected areas.Item Robust Regression Methods for Solving Non-Spherical Problem in Linear Regression(Sretech Journal Publications, 2019) Gatta, N. F.; Yahya, W. B.; Garba, M. K.This study investigated the effects of non-spherical disturbance on the model parameters of some classical regression models. The aim was to examine the impacts of multicollinearity on the efficiency of classical Ordinary least squares (OLS) relative to the ridge regression (RR) and principal component regression (PCR) models. Data were simulated from a multivariate normal distribution with mean zero and variance-covariance matrix at various sample sizes 25, 50, 100, 200, 500 and 1000. To assess the asymptotic efficiency and consistency of these regression models in the presence of multicollinearity, the evaluation criteria used were the Variance, Absolute bias, Mean Square Error (MSE) and Mean Square Error of Prediction (MSEP). Results from this work showed that the RR model had smaller variance, absolute bias and MSE when it was compared with OLS. Also, the ridge estimator had the least MSEP when compared to both the OLS and PCR models. Hence, it can be concluded that the ridge estimator performed better than the OLS and PCR when explanatory variables are highly correlatedItem A Test Procedure for Ordered Hypothesis of Population Proportions Against a Control(Turkish Clinical publications, Turkey, 2016) Yahya, W. B.; Olaniran, O. R.; Garba, M. K.; Oloyede, I.; Banjoko, A. W.; Dauda, K. A.; Olorede, K. O.Objective: This paper aims to present a novel procedure for testing a set of population proportions against an ordered alternative with a control. Material and Methods: The distribution of the test statistic for the proposed test was determined theoretically and through Monte-Carlo experiments. The efficiency of the proposed test method was compared with the classical Chi-square test of homogeneity of population proportions using their empirical Type I error rates and powers at various sample sizes. Results: The new test statistic that was developed for testing a set of population proportions against an ordered alternative with a control was found to have a Chi-square distribution with non-integer values degrees of freedom v that depend on the number of population groups k being compared. Table of values of v for comparing up to 26 population groups was constructed while an expression was developed to determine v for cases where k > 26. Further results showed that the new test method is capable of detecting the superiority of a treatment, for instance a new drug type, over some of the existing ones in situations where only the qualitative data on users’ preferences of all the available treatments (drug types) are available. The new test method was found to be relatively more powerful and consistent at estimating the nominal Type I error rates (α), especially at smaller sample sizes than the classical Chi-square test of homogeneity of population proportions. Conclusion: The new test method proposed here could find applications in pharmacology where a newly developed drug might be expected to be more preferred by users than some of the existing ones. This kind of test problem can equally exist in medicine, engineering and humanities in situations where only the qualitative data on users’ preferences of a set of treatments or systems are available.Item The Trade-off between the PLSR and PCR Methods for Modeling Data with Collinear Structure(Nigerian Association of Mathematical Physics, 2017-01-20) Yahya, W. B.; Olorede, K. O.; Garba, M. K.; Banjoko, A. W.; Dauda, K. A.