DEPARTMENT OF STATISTICS

This study focuses on the development of continuous lifetime distribution to model real life data sets. One approach to creating new distributions is the T-X (Tranformer- Transformed) method, which involves either adding a number of parameters to an existing distribution, raising a distribution to a power or combining existing distributions. In this study, the Paralogistic-Chen distribution is generated using the T-X (Transformer- Transformed) method of obtaining distributions. This involves a combination of the paralogistic and the Chen distributions. Some of the properties of the Paralogistic-Chen distribution are considered in this study and the application of the distribution will be considered to show how well the distribution fits the data and the Maximum Likelihood Estimation (MLE) is used to obtain the parameters of the distribution.

In kernel density estimation, the choice of kernel plays a crucial role in accurately estimating the underlying probability density function. This project focuses on comparing three commonly used kernels: Gaussian, Epanechnikov, and Biweight. The objective is to plot a graph that visually demonstrates the differences between these kernels and evaluate their efficiency using the mean square error metric. First, the theoretical foundations of kernel density estimation are explored, emphasizing the importance of choosing an appropriate kernel. The Gaussian kernel, known for its smoothness and symmetry, is widely used due to its desirable properties. The Epanechnikov kernel, with its compact support and optimal bias-variance trade-off, is another popular choice. Lastly, the Biweight kernel, which balances robustness and efficiency, is considered. To compare these kernels, a graph is plotted to visualize their shapes and characteristics. This graphical representation allows for a clear understanding of how each kernel affects the density estimation. Additionally, the mean square error metric is employed to quantitatively assess the efficiency of each kernel. By calculating the squared differences between the estimated density and the true density, the mean square error provides a measure of accuracy. Through this analysis, valuable insights into the strengths and weaknesses of each kernel can be gained. The graph and mean square error comparisons reveal how the choice of kernel impacts the estimated density function. This information can guide researchers and practitioners in selecting the most suitable kernel for their specific applications. Overall, this project contributes to a deeper understanding of the choice of kernel in kernel density estimation. By focusing on the Gaussian, Epanechnikov, and Biweight kernels, both their graphical representations and efficiency evaluations shed light on their performance in estimating probability density functions.

This study investigates the relationship between JAMB and Post-UTME scores at the University of Benin for the 2021/2022 academic session. Using quantitative methods, it explores the correlation and regression between these scores and their predictive power for academic performance. Reviewing existing literature, the study underscores the importance of considering both scores in admissions. Analysis reveals a positive significant but very low correlation between JAMB and PUTME scores and demonstrates JAMB scores having a weak predictive ability for Post-UTME performance. The study advocates for multi-measure assessment in admissions and concludes with recommendations for future research and policy improvements

This project work conducts a study on graduation of mortality rate using difference equation. The study illustrated the use of difference equation with an example solved manually and with the use of SPSS statistical software. The study started by introducing graduation, smoothness, mortality rates and some measures of mortality. We also looked at the methods of graduation, types of graduation and their advantages and disadvantages. We also looked at the test of graduation, where we considered two test which are the sign test and the chi-square test. Furthermore, the study looked at the meaning of difference equation, and we saw a few examples of difference equation. Methods of solving difference equation were also looked into Finally, illustrations were used to show how graduation of mortality rates works and results showed how we can predict ones death by how old he/she lives using the provided datasets.

In kernel density estimation, the choice of kernel plays a crucial role in accurately
estimating the underlying probability density function. This project focuses on
comparing three commonly used kernels: Gaussian, Epanechnikov, and Biweight. The objective is to plot a graph that visually demonstrates the differences between these kernels and evaluate their efficiency using the mean square error metric. First, the theoretical foundations of kernel density estimation are explored, emphasizing the importance of choosing an appropriate kernel. The Gaussian kernel, known for its smoothness and symmetry, is widely used due to its
desirable properties. The Epanechnikov kernel, with its compact support and
optimal bias-variance trade-off, is another popular choice. Lastly, the Biweight
kernel, which balances robustness and efficiency, is considered. To compare these kernels, a graph is plotted to visualize their shapes and characteristics. This graphical representation allows for a clear understanding of how each kernel affects the density estimation. Additionally, the mean square error metric is employed to quantitatively assess the efficiency of each kernel. By calculating the squared differences between the estimated density and the true density, the mean square error provides a measure of accuracy. Through this analysis, valuable insights into the strengths and weaknesses of each kernel can be gained. The graph and mean square error comparisons reveal how the choice of kernel impacts the estimated density function. This information can guide researchers and practitioners in selecting the most suitable kernel for their specific applications. Overall, this project contributes to a deeper understanding of the choice of kernel in kernel density estimation. By focusing on the Gaussian, Epanechnikov, and Biweight kernels, both their graphical representations and efficiency evaluations shed light on their performance in estimating probability density functions

This study investigates the relationships between economic growth, governmentexpenditure, and interest rates in Nigeria, employing various statistical methods. The research aims to provide actionable insights into the interactions betweenthesecrucial macroeconomic variables and their implications for policymaking. The theoretical foundation draws from Wagner's Law and the KeynesianFramework, which offer contrasting perspectives on whether governmentexpenditure is a cause or effect of economic growth. Using data fromtheCentralBank of Nigeria and the World Bank, the study employs the AugmentedDickey-Fuller (ADF) unit root test to assess stationarity, the Granger causalitytest toexamine causal relationships, and Ordinary Least Squares (OLS) regressiontoanalyze the effects of interest rates and government expenditure onGrossDomestic Product (GDP). The findings confirm the applicability of Wagner's Law in the Nigeriancontext, indicating that economic growth granger-causes government spending. Furthermore, the analysis reveals a positive relationship between interest rates, government expenditure, and GDP, although the results are not statisticallysignificant. The study highlights the importance of interest rates as apolicyinstrument for influencing economic performance and attractingforeigninvestment. To enhance the statistical robustness of the analysis, the study incorporatestheAnalysis of Variance (ANOVA) table, demonstrating its effectivenessin xi evaluating and improving the performance of regression models. The researchculminates in actionable recommendations for policymakers, emphasizingtheneedfor strategic fiscal policies, careful interest rate management, andtargetedinvestments in sectors that foster economic growth. Overall, this study contributes to the understanding of the intricate dynamicsbetween economic growth, government expenditure, and interest rates inNigeria, providing valuable insights for policymakers and researchers alike.

This study statistically examined the impact of choice of study programme, gender, age at admission, and ethnic affiliation on students’ academic performance in the University of Benin. The main objective was to determine the extent to which these variables influence students’ academic outcomes. A quantitative research design was adopted, and data were collected from undergraduate students across various faculties using structured questionnaires. The data were analyzed using the Statistical Package for the Social Sciences (SPSS) through descriptive statistics, chi-square test of independence and multiple regression analysis. The results revealed that the first choice of study programme had a significant influence on students’ academic performance, indicating that students who were given their first choice performed better than those who were placed in programmes by external influence. However, the demographic variables—gender, age at admission, and ethnic affiliation—did not show
statistically significant effects on academic performance. This implies that while demographic characteristics may influence students’ experiences, they do not independently determine academic achievement in the University of Benin based on this study. The study concludes that academic performance is more strongly influenced by students’ motivation and programme alignment as encapsulated in their first choice course of study than by demographic differences.

This study investigates the intricate relationship between psychological well-being and academic performance among students at the University of Benin. The research explores the impact of psychological issues such as anxiety, stress, and depression on students' academic journeys, as well as the influence of factors like parental roles and social support on their psychological well-being and academic success. A total of 377 students from various academic programs participated in the study, with statistical analysis, including the Spearman Rank Correlation test, used to extract meaningful insights and Statistical software SPSS used in analyzing data. The Findings drawn from this research are as follows: First, there is a significant correlation between psychological dysfunction, characterized by anxiety, stress, and depression, and students' academic performance. This emphasizes the need to address students' psychological well-being to enhance their academic success. Second, strong parental support plays a crucial role in mitigating psychological dysfunction, positively influencing academic performance. Lastly, fostering social support networks among students contributes to reduced psychological dysfunction and improved academic performance. Based on these insights, the study recommends enhancing psychological support services within the University of Benin, promoting parental engagement programs, and nurturing social support networks among students. These efforts can collectively contribute to students' holistic development, ensuring both their well-being and academic achievements.

In this project work, we look at how the least-square polynomial regression model is used to fit a non-linear relationship between a response variable and an explanatory variable in curve fitting. Finding a mathematical equation or model that best fits a noisy data has experience some drawback in curve fitting. i.e. finding an appropriate fit that best depicts the behaviour of the data. The purpose of this project is to show how the polynomial regression model can be used to show the relationship that exist between two variables; where the linear regression model is inadequate in describing such a relationship. The method of curve fitting used in this study is the least square polynomial regression method. It is designed in a way that, the model parameters are estimated by minimizing the residual term of the polynomial regression model; and then used the model to find the line that best fits the data points of the data set. This method was validated by modelling a data extracted from Nigeria Stock Exchange; and the model was able to predict over 80% of the relationship that existed in the data. It was discovered that the inadequacies of the simple linear regression model in describing the relationship that existed in a data set could be easily tackled by fitting a polynomial regression line. This is done by increasing the power of the independent variable to a higher power until we get a best fit

Lifetime data analysis plays a crucial role in various fields, ranging from engineering to epidemiology. In this study, we investigate the effectiveness of the Paralogistic-Weibull distribution in modeling lifetime data compared to other competing distributions such as the Weibull and Paralogistic distributions. Two datasets were analyzed: the daily number of COVID-19 infected persons in Nigeria and the survival times of patients with Head and Neck Cancer. We employed goodness-of-fit tests, including the Kolmogorov-Smirnov, Anderson-Darling, and Cramér-von Mises tests, along with discrepancy criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), to evaluate the performance of the distributions. The results indicate that the ParalogisticWeibull distribution consistently outperforms the other distributions across both datasets, exhibiting higher p-values and lower discrepancy criteria values. Therefore, we conclude that the Paralogistic-Weibull distribution offers superior flexibility and accuracy in modeling lifetime data, providing valuable insights for practitioners and researchers in the field of lifetime data analysis.