DEPARTMENT OF STATISTICS

This study investigates the effectiveness of Winsorization, a statistical technique used to handle outliers in data analysis. Outliers can significantly distort statistical measures such as the mean, variance, and standard deviation, leading to inaccurate conclusions and decision-making. The research applied Winsorization to three different datasets representing employee income, monthly product sales, and customer complaints to assess its impact on mitigating the effects of outliers. In each case, extreme values were adjusted to a more reasonable range, resulting in more reliable statistical results and better representation of the underlying data distribution. The analysis demonstrated that Winsorization effectively reduced the influence of outliers on central tendency and variability measures, making the data more representative of the majority. The study highlights the importance of data cleaning techniques like Winsorization in business contexts, ensuring more accurate analysis and informed decision-making. The findings also suggest that further research is needed to explore optimal levels of Winsorization and its application in larger, more complex datasets. This research contributes to the understanding of how data preprocessing can improve the integrity of statistical analyses in various business environments.

This research investigates the impact of smoking, level of exercise, and weight on health outcomes. The research employs a cross-sectional research design to investigate the associations between smoking, level of exercise, weight, and health outcomes among adults residing in Uyo Local Government Area, Akwa Ibom State, Nigeria. The study population comprises 360 adults, with a sample size of 124 determined using Taro Yamane’s sample size determination formula. Data collection involves a self-administered questionnaire covering demographic information, smoking habits, physical activity levels, weight, height, and health status. Convenience sampling is utilized at various locations within each of the four clans in Uyo LGA, facilitated by trained research assistants. Statistical Package for Social Sciences (SPSS) is employed for data analysis, including regression analysis to determine the relationships between independent variables (smoking, lack of regular exercise, weight) and the dependent variable (health outcome).The analysis reveals significant associations between these lifestyle factors and health outcomes, highlighting the need for targeted interventions to mitigate their adverse effects. Findings indicate a moderate positive correlation between smoking and health outcomes, emphasizing the importance of smoking cessation interventions. Similarly, a significant positive relationship is observed between lack of regular exercise and health outcomes, underscoring the importance of promoting physical activity. Additionally, the analysis reveals a moderate positive correlation between weight and health-related quality of life, emphasizing the need for interventions to promote healthy weight management.

Lifetime distributions are fundamental tools in statistics and probability theory, widely used to model the time until an event of interest occurs, such as the failure of a system, the death of an organism, or the occurrence of a financial default. This study focuses on reviewing three key lifetime distributions: The Exponential, Weibull, and Gamma distributions with an emphasis on their mathematical formulations, properties, and practical applications. The Exponential distribution, characterized by its memoryless property and constant hazard rate, is simple but limited in its applicability to more complex scenarios. The Weibull distribution, with its flexibility in modeling increasing, decreasing, or constant hazard rates, is highly versatile and widely used in reliability engineering. The Gamma distribution, capable of modeling multi-phase processes, is particularly useful for analyzing skewed data and complex lifetime behaviors. This study contributes to the theoretical understanding of lifetime distributions and provides practical guidelines for their application in fields such as reliability engineering, survival analysis, and risk assessment. Recommendations for future research include exploring additional distributions, analyzing larger datasets, and applying advanced estimation methods to further enhance the accuracy and applicability of lifetime distribution models.

This was an empirical study to determine the usage and impact of social media on academic learning and performance of undergraduates of University of Benin students. To achieve this general objective, four research questions was raised and four null hypotheses formulated, which guided the study. A survey research design was used for the research. Questionnaire was used to generate primary data from a representative random sample of 150 students (100 representing 100 percent was correctly filled and returned). The students who participated in the survey were drawn from various faculties in the University. Descriptive statistics of frequency counts and percentages were used in analysing demographic variables and research questions while Chi-Square (X2) were used to test the stated hypotheses at a 0.05 level of significance. The results and contributions to knowledge include that the most common reason for social media usage to keep up with trending issues on news and sports as well as to access an incredible amount of valuable information on a variety of topic, also that there is a significant relationship between social media usage and student academic performance; a significant difference between male and female students usage of social media; and that age has a significant relationship with social media usage. It was recommended that parents and guardians should help to ensure that students utilize the benefits of social media and that scholars and opinion leaders should make effort to educate undergraduates to minimize time wastage on frivolities (chatting, cyber stalking, etc.) and other irrelevant engagements that are not of major importance in their academic lives.

This study delves into the Gompertz distribution, a versatile probability distribution with applications in survival analysis, population dynamics, and reliability modeling. The research explores how its behavior is influenced by two crucial parameters, 'a' and "b,' and how variations in these parameters impact statistical properties. The analysis covers theoretical and sample-based metrics, providing insights into central tendency, spread, shape, and more through tables, graphs, and histograms. The results indicate that changes in 'a' and 'b' parameters systematically alter the distribution's characteristics, while sample size affects parameter estimations. This work equips readers with a deep understanding of the Gompertz distribution's dynamics, aiding informed decisions in practical applications across diverse fields.

This study investigates the application of Exponential, Weibull, and Gamma distributions in modeling lifetime data. The primary objective is to compare these distributions in real world survival analysis and reliability modeling. The study utilizes secondary data from published research, including survival times of head and neck cancer patients and waiting times of bank customers .
Maximum Likelihood Estimation (MLE) was employed to estimate distribution parameters, and model comparisons were performed using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to determine the best fitting distribution.

Findings reveal that while the Exponential distribution provides a simple model for constant failure rates, the Weibull distribution offers greater flexibility in modeling varying failure rates. The Gamma distribution demonstrates robust applicability in complex survival data. Results indicate that the Weibull and Gamma distributions provide superior fits in most real world cases.
This study contributes to the field of survival analysis and reliability engineering by providing insights into selecting appropriate lifetime distributions for different applications. The findings have practical implications for fields such as healthcare, engineering, and risk assessment, where accurate lifetime modeling is crucial for decision making.

Statistical quality characteristics of the components are determined process can be selected for manufacture of the components. In mass production, products are assembled using parts or components manufactured or processed on different process or machines. This requires complete interchangeability of parts while assembling them, on the other hand, there will always be variations in the quality characteristics [length, weight, thickness etc.] because of the inherit variability introduced by the machines, tools, raw materials and operators. The presence of unavoidable variation and the necessity of interchangeability require that some limits be specified for the variation for any quality characteristic. A statistical control and loss minimization approach is a way of using statistical methods to minimize the total cost of quality including the cost of the defects and cost of controlling the process. this approach involves setting quality standards, collecting data on product or services characteristics, analysing the data to detect problems and then correcting these problems. This approach also helps organization achieve the highest possible quality at the lowest possible cost. The need of Statistical quality control in product and services cannot be over emphasized, as it helps in the improvement of manufacturing process to meet customer satisfaction.

This study investigates the relationship between crop performance, fertilizer application, and soil types using multivariate statistical analysis. The main objective is to determine how different fertilizer types and the rate of application, in combination with soil characteristics, influence major growth and yield parameters of crops. Data were collected on soil properties
(such as pH, organic matter, nitrogen, phosphorus, potassium, and texture) and crop growth parameters (including germination percentage, plant height, number of leaves, leaf area, biomass, and yield). The canonical correlation analysis was employed to identify patterns and quantify the strength of associations among these variables. The results revealed that soil fertility factors and fertilizer applications significantly influenced crop growth and yield performance, with organic matter and fertilizer rate producing optimal responses. The analysis demonstrates the usefulness of Canonical Correlation Analysis in handling complex agricultural data.

Nosocomial infections, also known as hospital-acquired infections, are bacterial infections contracted within healthcare settings. They contribute significantly to the burden of disease by prolonging hospital stays, increasing treatment costs, complicating surgical outcomes, and, in severe cases, leading to death. Methicillin resistant staphylococcus aureus (MRSA) is the most isolated
pathogen of nosocomial infections and the most studied in the literature. Despite their impact, awareness of nosocomial infections remains limited, leaving patients, healthcare workers, visitors, and even family caregivers vulnerable to its transmission. In low-income and middle-income countries the practice of a family caregiver assisting an inpatient is common, and they can contact and transmit infections while carrying out various activities within the hospital environment. Deterministic and stochastic models have been widely applied to understand the transmission dynamics of nosocomial infections and provide valuable insights. However, existing models have often overlooked the role of patients’ family caregivers, who can act as important but underrecognized vectors of transmission. In this thesis, deterministic and stochastic models that explicitly incorporate family caregivers as a distinct transmission pathway of methicillin-resistant Staphylococcus aureus (MRSA) are developed. For the deterministic framework, the basic reproduction number �0 is derived along with the conditions for disease-free and endemic equilibria. The stochastic framework developed using a Continuous-time Markov Chain (CTMC) extends the deterministic model by incorporating random fluctuations through its drift and diffusion terms. This provides deeper insight into the system’s variability, extinction probabilities, and outbreak risks that cannot be fully captured by the deterministic model. For the deterministic model, the basic reproduction number is evaluated and subjected to sensitivity analysis, using plausible parameter values from surveillance studies within Nigerian hospitals, whereby revealing the dominant influence of hand-hygiene compliance of caregivers and healthcare workers, as well as decontamination rates of both caregivers and healthcare workers. The stochastic simulation in MATLAB gives the stochastic sample paths, time-series behaviours of the state variables and extinction probability. The numerical results illustrate that while the deterministic model captures mean epidemic behaviours, stochastic models reveal substantial variability and probability of infection extinction especially in settings with effective hand hygiene compliance of caregivers and healthcare workers. These analyses reveal the importance of integrating patients’ family caregivers in modeling the spread of MRSA in hospitals.

The exponential distribution became the cornerstone of survival analysis and reliability engineering throughout the latter half of the 20th century and it is imperative to mention that the Successive times in exponential distribution are assumed to occur independently and randomly over time with a constant rate. The aim of the study was to develop a generalized and flexible bivariate exponential distribution that will incorporate correlation parameter 𝜌, extending the domain to a positive real-line using the framework of linear regression. A secondary dataset from Federal Road Safety Corps on road accidents in Imo State from 2020 to
2024 was used in the study and it was obtained from the Head office of Federal Road Safety Corps, off Egbu road Owerri, Imo state. In the study, we developed a generalized and bivariate exponential model that incorporates a correlation parameter, while preserving analytical simplicity. The proposed model, referred to as the New Correlated Bivariate Exponential Distribution (NCBED). The consistency of the NCBED was assessed using Kolmogorov Smirnov and Cramer Von Mises tests, in comparison with the baseline Grine model (2018). The Federal Road Safety (FRSC) dataset demonstrates that both injury and fatality data follow heavy-tailed exponential-type distributions and the NCBED provided a superior fit compared to the baseline model, capturing real-world correlations between crash outcomes. The findings indicate that the Maximum Likelihood estimates of the proposed model are consistent with the nature of the model.