Department oF Mathematics and Statistics

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A Comparative Analysis of Semiparametric Tests for Fractional Cointegration in Panel Data Models
(Austria Statistical Society, 2022) Saidat Fehintola Olaniran; Mohd Tahir Ismail
Several authors have studied fractional cointegration in time series data, but little or no consideration has been extended to panel data settings. Therefore, in this paper, we compare the finite sample behaviour of existing fractional cointegration time-series test procedures in panel data settings. This comparison is performed to determine the best tests that can be adapted to fractional cointegration in panel data settings. Specifically, simulation studies and real-life data analysis were performed to study the changes in the empirical type I error rate and power of six semiparametric fractional cointegration tests in panel settings. The various results revealed the limitations of the tests in the nonstationary and low or high correlation of the residual errors conditions. Also, two of the test procedures were recommended for testing the null hypothesis of no fractional cointegration in both time series and panel data settings.
A Comparative Study on Zero-truncated Generalized Poisson-Lindley and Zero-truncated Poisson-Lindley Distributions
(International journal of Mathematical Archive (IJMA), 2017) Aderoju, S.A.; Jolayemi, E.T.; Ibrahim, A.O.
In this paper, Zero-truncated Com-binomial distribution was derived and investigated its behavior in modeling structurally non-zero data. The proposed distribution is characterized by two parameters, which make it flexible. The maximum likelihood method is used to obtain the estimators of the parameters through R-software. Two real-life datasets were used to evaluate its performance. The statistic (chi square goodness-of-fit) with the p-value shows that the proposed Zero-truncated Com-binomial distribution yields “a good fit”.
A GENERALIZED SCHEME FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS BY THE RECURSIVE FORMULATION OF TAU METHOD
(2013-05) K. Issa; R.B. Adeniyi
The generalization of the recursive form of the tau method for both overdetermined and non-overdetermined ordinary differential equations of the initial value type is the main thrust of the work reported here. This will facilitate an automation of this variant of the method and consequently an efficient utilization of the technique. Results from the numerical experiment confirm the validity and effectiveness of the derived scheme.
A New Generalized Gamma-Weibull Distribution and its Applications
(Al-Bahir Journal for Engineering and Pure Sciences, 2023-04-17) Aleshinloye, N.I.; Aderoju, S. A.; Abiodun, A.A.; Taiwo, B.L.
In this paper, a New Generalized Gamma-Weibull (NGGW) distribution is developed by compounding Weibull and generalized gamma distribution. Some mathematical properties such as moments, Renyi entropy and order statistics are derived and discussed. The maximum likelihood estimation (MLE) method is used to estimate the model parameters. The proposed model is applied to two real-life datasets to illustrate its performance and flexibility as compared to some other competing distributions. The results obtained show that the new distribution fits each of the data better than the other competing distributions.
A New Generalized Gamma-Weibull Distribution with Applications to Time-to-event Data
(2023-11-18) Kazeem Adesina Dauda; Rasheed Kehinde Lamidi; Adeshola Adediran Dauda; Waheed Babatunde Yahya
In this research, a new class of probability distributions referred to as Generalized Gamma Weibull (GGW) distributions was introduced within the context of parametric survival analysis. This distribution represents a modification of the gamma Weibull distribution and offers valuable insights, particularly when dealing with highly skewed lifetime data. The study extensively examined the mathematical characteristics of these distributions, encompassing hazard functions, moments, quantile functions, and order statistics. Furthermore, the research delved into parameter estimation methods for these newly proposed distributions, employing the maximum likelihood technique, Fisher Information (FI), and deriving asymptotic confidence intervals for both censored and uncensored scenarios. To illustrate the practical utility of these proposed distributions, the study applied them to analyze two sets of real-life survival data and two sets of real-life data, resulting in a total of four distinct datasets. To gauge the effectiveness of the GGW distributions in comparison to existing methods such as Generalized Weibull and Generalized gamma (G-Weibull and G-Gamma) distributions, the research employed statistical indices including the Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), and Bayesian Information Criterion (BIC). The outcomes of this comparative analysis demonstrated the superior performance of the newly introduced GGW distributions (AIC=338.6313, BIC=346.2794, and CAIC=339.5202) when contrasted with the existing methods (G-Weibull: AIC=376.1946, BIC=381.9307, and CAIC=376.5424) across all three criteria, thereby highlighting the enhanced suitability of GGW distributions for modeling and analyzing skewed lifetime data.
A new generalized Poisson mixed distribution and its application
(Applied Mathematical Sciences, 2020) Aderoju, S.A.
A new generalized Poisson mixed distribution is proposed in this study called New Generalized Poisson-Sujatha distribution (NGPSD). The properties and application of the distribution are studied. The two parameter distribution is obtained by compounding Poisson distribution with a two parameter generalized Sujatha distribution. The distribution has a tendency to account for over-dispersion in count data. The first four moments, variance and coefficient of variation of the distribution are also obtained. The estimators of its parameters are obtained via maximum likelihood method using R-software. The goodness-of-fit of the distribution is compared with other distributions such as Poisson distribution (PO), negative binomial (NB), Generalized Poisson-Lindley (GPL) and a New Generalized Poisson-Lindley (NGPL) Distributions. It can be seen that the test statistic, AIC and BIC for the NGPSD are lower than those of competing distributions implying that the proposed distribution satisfactorily fits better to the data set.
A New Lifetime Distribution and its Application to Cancer Data
(Journal of Biostatistics and Epidemiology, 2023-12-15) Samuel Adewale Aderoju; Nihimat Iyebuhola Aleshinloye; Bako Lukmon Taiwo; Bello Ishola Sanni
Introduction: Recently, researchers have introduced new generated families of univariate lifetime distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution or compounding two distributions to get more flexibility in fitting data in different areas such as medical sciences, environmental sciences, and engineering. The addition of parameter(s) has been proven useful in exploring tail properties and for improving the goodness-of-fit of the family of the proposed distributions. Methods:A new Three-Parameter Weibull-Generalized Gamma distribution which provides more flexibility in modeling lifetime data is developed using a two-component mixture of Weibull distribution (with parameters θ and λ) and Generalised Gamma distribution (with parameters α=4,θ and λ). Some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, moment generating function, Renyi entropy and order statistics are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters. Results: Real life applications of the proposed distribution to two cancer datasets are presented and its fit was compared with the fit attained by some existing lifetime distributions to show how the Three-Parameter Weibull-Generalized Gamma distribution works in practice. Conclusion: The results suggest that the proposed model performed better than its competitors and it’s a useful alternative to the existing models.
A novel hybrid dimension reduction technique for efficient selection of bio-marker genes and prediction of heart failure status of patients
(Scientific African, 2021-05-02) Kazeem Adesina Dauda; Kabir Opeyemi Olorede; Samuel Adewale Aderoju
This study highlighted and provided a conceptual framework of a hybridized dimension reduction by combining Genetic Algorithms (GA) and Boruta Algorithm (BA) with Deep Neural Network (DNN). Among questions left unanswered sufficiently by both computational and biological scientists are: which genes among thousand of genes are statistically relevant to the prediction of patients’ heart rhythm? and how they are associated with heart rhythm? A plethora of models has been proposed to reliably identify core informative genes. The premise of this present work is to address these limitations. Five distinct micro-array data on heart diseases have been taken into consideration to observe the prominent genes. We form three distinct set two-way hybrids between Boruta Algorithm and Neural Network (BANN); Genetic Algorithm and Deep Neural Network (GADNN) and Boruta Algorithm and Deep Neural Network (BADNN), respectively, to extract highly differentially expressed genes to achieve both better estimation and clearer interpretation of the parameters included in these models. The results of the filtering process were observed to be impressive since the technique removed noisy genes. The proposed BA algorithm was observed to select minimum genes in the wrapper process with about 80% of the five datasets than the proposed GA algorithm with 20%. Moreover, the empirical comparative results revealed that BADNN outperformed other proposed algorithms with prediction ac curacy of 97%, 87%, and 100% respectively. Finally, this study has successfully demonstrated the utility, versatility, and applicability of hybrid dimension reduction algorithms (HDRA) in the realm of deep neural networks.
A Novel Hybrid Dimension Reduction Technique for Efficient Selection of Bio-marker Genes and Prediction of Heart Failure Status of Patients
(Elsevier, 2021) Dauda K. A.; Olorede K. O.; Aderoju S. A.
This study highlighted and provided a conceptual framework of a hybridized dimension reduction by combining Genetic Algorithms (GA) and Boruta Algorithm (BA) with Deep Neural Network (DNN). Among questions left unanswered sufficiently by both computational and biological scientists are: which genes among thousand of genes are statistically relevant to the prediction of patients’ heart rhythm? and how they are associated with heart rhythm? A plethora of models has been proposed to reliably identify core informative genes. The premise of this present work is to address these limitations. Five distinct micro-array data on heart diseases have been taken into consideration to observe the prominent genes. We form three distinct set two-way hybrids between Boruta Algorithm and Neural Network (BANN); Genetic Algorithm and Deep Neural Network (GADNN) and Boruta Algorithm and Deep Neural Network (BADNN), respectively, to extract highly differentially expressed genes to achieve both better estimation and clearer interpretation of the parameters included in these models. The results of the filtering process were observed to be impressive since the technique removed noisy genes. The proposed BA algorithm was observed to select minimum genes in the wrapper process with about 80% of the five datasets than the proposed GA algorithm with 20%. Moreover, the empirical comparative results revealed that BADNN outperformed other proposed algorithms with prediction accuracy of 97%, 87%, and 100% respectively. Finally, this study has successfully demonstrated the utility, versatility, and applicability of hybrid dimension reduction algorithms (HDRA) in the realm of deep neural networks.
A Novel Variable Selection Procedure for Binary Logistic Regression Using Akaike Information Criteria Testing: An Example in Breast Cancer Prediction.
(Turkiye klinikleri, 2023-07-13) Oyebayo Ridwan Olaniran; Saidat Fehintola Olaniran
Breast cancer is a leading cause of cancer-related death among women worldwide, with approximately 2.3 million new cases and 685,000 deaths reported in 2020 alone. One critical step in developing effective classification and prediction models is variable selection, which involves identifying a subset of relevant variables from a larger set of potential predictors. Accurate variable selection is crucial for building interpretable and robust models that are not overfit to noise, leading to improved model performance and generalization ability. In this paper, we proposed an alternative objective approach for comparing two Akaike Information Criterions (AIC) that originated from two competing models, such that the magnitude of the difference is subjected to the statistical test of significance. Material and Methods: We developed a new backward elimination variable selection procedure similar in spirit to the existing “step AIC” within the environment of R statistical software. We used both simulated and Wisconsin breast cancer diagnostic datasets to compare the proposed method's variable selection and predictive performances with “step AIC” and LASSO. Results: The simulation showed that the proposed AIC procedure achieved higher variable selection sensitivity, specificity and accu racy when compared to stepAIC and LASSO. Also, the proposed AIC method's prediction results are relatively comparable with ste pAIC and LASSO at various simulated data dimensions. Similar supremacy results were observed with the breast cancer dataset used. Conclusion: The AIC-based variable selection approach pro posed is a promising method that integrates AIC with statistical testing for improved variable selection in breast cancer classifica tion and predictio
A Test Procedure for Ordered Hypothesis of Population Proportions Against a Control
(Turkiye Klinikleri Journal of Biostatistics, 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: 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.
A two-step block method with two hybrid points for the numerical solution of first order ordinary differential equations
(2022-12-31) AbdulAzeez Kayode Jimoh; Adebayo Olusegun Adewumi
A continuous two-step block method with two hybrid points for the numerical solution of first order ordinary differential equations is proposed. The approximate solution in form of power series and its first ordered derivative are respectively interpolated at the point x = 0 and collocated at equally spaced points in the interval of consideration. The application of the method involves using the main scheme derived together with the additional schemes simultaneously to obtain the solution to the problem at the grid points. The analysis of the method and the results obtained from the examples considered show that the method is consistent, zero-stable, convergent and of high accuracy.
An algorithm for choosing best shape parameter for numerical solution of partial differential equation via inverse multiquadric radial basis function
(2020-04-30) Kazeem Issa; Sulaiman M. Hambali; Jafar Biazar
Radial Basis Function (RBF) is a real valued function whose value rests only on the distance from some other points called a center, so that a linear combination of radial basis functions are typically used to approximate given functions or differential equations. Radial Basis Function (RBF) approximation has the ability to give an accurate approximation for large data sites which gives smooth solution for a given number of knots points; particularly, when the RBFs are scaled to the nearly flat and the shape parameter is chosen wisely. In this research work, an algorithm for solving partial differential equations is written and implemented on some selected problems, inverse multiquadric (IMQ) function was considered among other RBFs. Preference is given to the choice of shape parameter, which need to be wisely chosen. The strategy is written as an algorithm to perform number of interpolation experiments by changing the interval of the shape parameters and consequently select the best shape parameter that give small root means square error (RMSE). All the computational work has been done using Matlab. The interpolant for the selected problems and its corresponding root means square errors (RMSEs) are tabulated and plotted.
An analogue of the tau method for ordinary differential equation
(2010) K. Issa; R. B. Adeniyi
In this paper, we construct three orthogonal polynomials which are incorporated into the perturbation term of a numerical scheme analogue to the Ortiz recursive formulation of the Lanczos tau method. The method was implemented on some selected problems and the accuracy obtained justifies the desirability of the numerical scheme.
An error estimation of a numerical scheme analogue to the tau method for initial value problems in ordinary differential equations
(2014-03) K. ISSA; A. K. JIMOH
In a recent paper, we constructed three classes of orthogonal polynomials for use in the perturbation term of a numerical integration scheme analogues to the tau method of Lanczos and Ortiz for ordinary differential equations. The resulting n-th degree approximant y_n(x) of the solution y(x) of the differential equation was accurate and hence justified the scheme. In this present paper, we report an error estimation of the method based on our earlier work. The estimate obtained is good as it correctly captured the order of the tau approximant.
An Exploratory Analysis of Human Immunodeficiency Virus (HIV) Prevalence in Nigeria
(2023) Saidat Fehintola Olaniran; Risikat Ayodeji Bello
This paper involved conducting a statistical analysis on the number of individuals living with HIV/AIDS. The University of Ilorin Teaching Hospital (UITH) was chosen as the case study for the years 2014 to 2019, with factors such as year, sex, and age group taken into account. During this six-year period, a total of 2604 cases were recorded at UITH. Among both sexes, females had the highest number of people living with HIV/AIDS. Additionally, the age group of 31-45 had the highest number of individuals affected by the disease. In terms of the specific year, 2016 had the highest number of people living with the disease, totalling 460 cases. A chi-square test of independence was conducted to examine the relationship between the factors, using a significance level of 0.05. The results indicated that all the considered factors were not independent of each other, meaning they were related.
An Exploratory Analysis of Human Immunodeficiency Virus (HIV) Prevalence in Nigeria.
(Scretech, 2023-06) Saidat Fehintola Olaniran; Risikat Ayodeji Bello
This paper involved conducting a statistical analysis on the number of individuals living with HIV/AIDS. The University of Ilorin Teaching Hospital (UITH) was chosen as the case study for the years 2014 to 2019, with factors such as year, sex, and age group taken into account. During this six-year period, a total of 2604 cases were recorded at UITH. Among both sexes, females had the highest number of people living with HIV/AIDS. Additionally, the age group of 31-45 had the highest number of individuals affected by the disease. In terms of the specific year, 2016 had the highest number of people living with the disease, totaling 460 cases. A chi-square test of independence was conducted to examine the relationship between the factors, using a significance level of 0.05. The results indicated that all the considered factors were not independent of each other, meaning they were related.
Analytical Solution of Generalized Fractional Integro-Di erential Equations via Shifted Gegenbauer Polynomials
(MATEMATIKA, MJIAM, Volume 40, Number 3, 113{129 c Penerbit UTM Press. All rights reserved, 2024-12-31) Kazeem Issa; Adebayo Ridwan; Muritala Hambali Sulaiman
Abstract In this paper, we proposed an analytical solution for generalized fractional order integro-di erential equations with non-local boundary conditions via shifted Gegenbauer polynomials as an approximating polynomial using the Galerkin method and collocation techniques involving operational matrix that make use of the Liouville-Caputo operator of differentiation in combination with Gegenbauer polynomials. Shifted Gegenbauer polynomial properties were exploited to transform fractional order integro-differential equation and its non-local boundary conditions into an algebraic system of equations. Shifted Gegenbauer polynomial C_m^((α) ) (x) was used in order to generate and generalize the results of some other orthogonal polynomials by varying the value of parameter . The accuracy and effctiveness of the proposed method are tested on some selected examples from the literature. We observed that, when the exact solution is in polynomial form, the approximate solution gives a closed form solution, and non-polynomial exact solution, also give better results compared to the existing results in the literature.
Analytical Solution of Some Non – Linear Delay Differential Equations Using Adomian Decomposition Method
(Department of Computer Engineering, Sigma University , Vadodara Gujarat, India, 2024) Lawal1*, O.J; Muraina, S.; Ibrahim, G. R.; Faruk ,M.; Idris, S.
This study examined some Non-linear Delay Differential Equation problems with known exact solutions and solved them using the Adomian Decomposition Method. We then observed the results and compared them with the corresponding exact solutions, and ultimately found that the two results agree. In addition, we discussed the phenomena that occur in real life and are described by Non-linear Differential Equations.
Application of Lattice Theory on Order-Preserving Full Transformation Semigroup Via Fixed Points
(Faculty of Physical Sciences, University of Ilorin, 2023) Ibrahim, G. R.1, Bakare, G. N.2, Akinwunmi. S. A.3and Aliu, O. T.
Let 𝑋𝑛be a finite set, 𝑇𝑛be full transformation semigroup and 𝑂𝑇𝑛be subsemigroup of all order-preserving full transformation semigroup. Let transformation𝛼∈𝑂𝑇𝑛∶(∀𝑥,𝑦∈Dom𝛼),if𝑥≤𝑦then𝛼(𝑥)≤𝛼(𝑦), then 𝛼is called order-preserving transformation. This paper focuses on the notion of fixed points which are elements that remain unchanged under this transformation. That is, 𝛼(𝑥)=𝑥where 𝛼is a transformation on 𝑂𝑇𝑛, 𝑥is the point in the 𝐷𝑜𝑚(𝛼)and 𝛼(𝑥)is the image of x,∀x∈αThe existence of fixed points was explored and emphasizing their role in establishing a lattice structure. The lattice of fixed points exhibits two essential operations: meet and join. These operations enable us to compute the greatest and least elements of fixed points. Beyond pure mathematics, the study of fixed points and their lattice structure has applications in dynamical systems, economics, computer science, and several other domains, making it both a theoretical and practical subject.

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