| 1 |
Author(s):
Ogbeide E.M., Shuaibu M., Siloko U.I..
Page No : 1-11
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Theory and Application of Two (2) Iterative Imputation Approaches to Nigeria Annual Rainfall Data Reported
Abstract
This research work is based on missing data statistics. Missing data occur where one or more of the observations in a dataset are completely not available. This work focuses on two (2) iterative imputation approaches. These are the Regression approach and the Expectation Maximization iterative imputation. These approaches were used to analyze the secondary data of the thirty-six (36) states in Nigeria on the rainfall data collected from the Annual Abstract of Statistics 2016. The evaluation criteria and comparison of these two approaches were done based on the error efficiency using the Raw Bias (RB), Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and variance. The analysis of the result showed that the Expectation Maximization (EM) method was better for this specific data as reported in the Annual Abstract of Statistics 2016, compared to the other approaches. This was seen in the smaller errors values from the computed cases. It is therefore recommended that this approach should be used for obtaining missing data like other rainfall data in Nigeria. These two imputation approaches are good for making available missing data in observations.
| 2 |
Author(s):
Edike Nnamdi, Osuji George Amaeze.
Page No : 12-33
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Comparative Study of the Gompertz and Logistic Growth Models on the Prevalence and Fatality of Covid-19 Pandemic in Nigeria
Abstract
This study models the prevalence and fatality of the Covid-19 pandemic in Nigeria from February 2020 to July 2022. It is a comparative study of two prominent models: The Gompertz and Logistic population growth models. The data for this study was obtained from the website of Our World in Data, OWID (https//www.ourworldindata.org). The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were employed to compare the performance of the models, and the number of iterations before convergence and convergence tolerance for each model was also put into consideration. The study revealed that the Gompertz population growth model provides a better fit compared to the logistic growth in modelling the cumulative covid-19 cases and cumulative covid-19-related deaths in Nigeria. From the models, we obtained important features of the pandemic, such as the growth rate and asymptotes.
| 3 |
Author(s):
U. P. Akra, O. E. Ntekim, G. S. Robinson, A. C. Etim.
Page No : 34-43
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Evaluation of Some Algebraic Structures in Balanced Incomplete Block Design
Abstract
Balanced incomplete block design is an incomplete block design in which any two varieties appear together an equal number of times. In algebra, the existence of block design is closely related to balanced incomplete block design. To ascertain the claim, this research aim to employ some algebraic structures to examine whether or not balanced incomplete block design is related to the above statement. The methods adopted are finite group, ring and field algebra. The result shows that balanced incomplete block design (BIBD) cannot form a finite group under multiplication binary operation, but it is for additive case. It is also revealed that balanced incomplete block design is not a field algebra in both binary operations no matter the size of the design, but it is a ring in all cases. In conclusion, BIBD of the form (X,B) is a semigroup, commutative group, semiring, commutative ring and subfield in both binary operations. Several theorems with proofs have been established in harmony with the algebraic structure mentioned above.
| 4 |
Author(s):
Udochukwu Victor Echebiri, Chinelo Ujunwa Anyadiegwu, Nosakhare Liberty Osawe, Hadiyya Abu Abubakar, Chinyere Josephine Adewole.
Page No : 44-62
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A New Logistic Generalization Arising from Distributions of Order Statistics: Properties and Applications
Abstract
Distributions with the variable support x∈R that exhibit strict symmetricity are versed in literature; and serve as model-fit for various forms of bell shaped outcomes; where normal and logistic distributions are renowned examples. This strictness, however, limits the application of these probability models to a particular kind of data; hence, its minimal utility. In this paper, therefore, a new generalization for the logistic distribution termed the Jones generalized logistic distribution is proposed. This new distribution is conditionally symmetric; which entails that the distribution attains symmetricity, only at equal parameter combinations. By implication, the proposed distribution serves the dual purpose of modeling both symmetric and asymmetric outcomes. Some properties of the proposed model have been derived. Finally, JGLD were fit to two different lifetime data as a demonstration to its relevance.
| 5 |
Author(s):
O. E. Ntekim, J. A. Ugboh, J. N. Ezeorah, U. P. Akra.
Page No : 63-67
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Well-Conditioned and Ill Conditioned Linear First Order Initial Value Problems in Ordinary Differential Equation
Abstract
We construct a linear first order ordinary differential equation with the parameter λ. We show that our constructed equation is well conditioned for λ 0. We also state and prove some related theorems.
| 6 |
Author(s):
Wiri Leneenadogo, Dr. Archibong Mark Edet.
Page No : 68-76
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Symmetry and Asymmetry Multivariate Garch Modeling of Consumer Prices Index, Crude Oil Price, Inflation Rate and Exchange Rate
Abstract
The study looked at changes in Nigeria's exchange rate, inflation rate, consumer price index, and price of crude oil. Monthly data from January 2004 to December 2020 were utilized in this analysis, and they were taken from the statistical bulletin of the Central Bank of Nigeria (CBN). The data's time graphic showed the trend series' present state. For the analysis, E-view 12 statistical software was employed. Modeling employed both symmetric and asymmetric processes. Using both symmetric and asymmetric modeling techniques, the Multivariate Generalized Autoregressive Conditional Heteroscedasticity (M-GARCH) model was developed. To estimate three models for multivariate GARCH, a constant conditional correlation, a diagonal VECH, and a diagonal BEKK. The conditional variance and conditional covariance were estimated using these models. Every variance and covariance model had a significance level of 5%.
| 7 |
Author(s):
Okoro Ifeanyichukwu, Uka Christian O., Ogbara Chidi Obed.
Page No : 77-80
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Application of Three Probability Distributions to Justify Central Limit Theorem
Abstract
This paper focused on the use of three probability distributions to justify the central limit theorem (CLT). The aim was to use the moment generating function (MGF) to prove (CLT) and also to portray the shape of different sample sizes (15, 30 and 100) of distributions of sample means on a histogram. The population distributions studied were: Normal, Gamma and Exponential distributions. In addition, sampling distribution of the mean table was constructed for better understanding of CLT. The study used simulation to simulate population distribution of Normal, Gamma and Exponential. Five hundred (500) distributions of sample means were drawn from each of the simulated population distributions at three different sample sizes (n): 15, 30 and 100. The shape of the simulated population distribution and sampling distribution of mean were presented on a histogram. The mean and standard deviation of each population distribution together with distribution of sample means at different sample sizes were also presented on the histogram plotted. The findings showed that under normal distribution, the sampling distribution of mean produced a shape like normal distribution irrespective of the sample size. Conversely, the shape of sampling distribution of mean under non-normal distributions gradually converges to normal distribution as sample size tends to infinity, while the variability of each sampling distribution decreases as the sample size increases. Therefore, CLT holds for large sample size (n ≥ 30).
| 8 |
Author(s):
Nwaokolo Martin Afam, Okorie Charity Ebelechukwu.
Page No : 81-90
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Assessing the Prevalence of Tuberculosis in Taraba State
Abstract
Tuberculosis is an old disease that poses a new threat and remains a public health issue in Nigeria, having been ranked as the second biggest cause of death from single infectious disease after HIV/AIDS. The world health organization initiated the stop TB programs and directly observed treatment short course centers to eliminate tuberculosis, yet tuberculosis in developing countries is still on the high side. Therefore, this work is primarily targeted at providing reliable and concrete information on the rate of occurrence and prevalent rate of TB in Taraba State. The aim of this research is to analyze the cases of TB in Taraba State. In order to carry out this research, data were collected from Specialist Hospital, Jalingo. The data collected were analyzed using the SPSS (Statistical Package for Social Science) software 16.0. Ordinary Least Square and Analysis of Variance (ANOVA) were used in carrying out the analysis. The analysis with the least square method yields the linear trend equation as y = 551.917 – 14.582x + e, where y = a + bx + e. X= 2(t-2013.5). This trend indicates that there is a falling trend. For instance, using the Linear Trend to forecast for the future, we discovered that there will be a decrease in tuberculosis from 2023 with the value of 413.388, 2024=399.806, 2025=384.228.
| 9 |
Author(s):
Ajinuhi J.O., Mohammed U., Enagi A.I., Jimoh O.R..
Page No : 91-112
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An Optimized Single-Step Block Hybrid Nyström-Type Method for Solving Second Order Initial Value Problems of Bratu-Type
Abstract
In this paper, a global single-step implicit block hybrid Nyström-type method (BHNTM) for solving nonlinear second-order initial-boundary value problems of Bratu-type is developed. The mathematical derivation of the proposed BHNTM is based on the interpolation and multistep collocation techniques with power series polynomials as the trial function. Unlike previous approaches, BHNTM is applied without linearization or restrictive assumptions. The basic properties of the proposed method, such as zero stability, consistency and convergence are analysed. The numerical results from three test problems demonstrate its superiority over existing methods which emphasize the effectiveness and reliability in numerical simulations. Furthermore, as the step size decreases as seen in the test problems, the error drastically reduces, indicating BHNTM's precision. These findings underscore BHNTM's significance in numerical methods for solving differential equations, offering a more precise and dependable approach for addressing complex problems.
