Olasunmbo O. Agboola

Gumbel Distribution: Ordinary Differential Equations

In this chapter, homogenous ordinary differential equations (ODES) of different orders were obtained for the probability density function, quantile function, survival function inverse survival function, hazard function and reversed hazard functions of Gumbel distribution. This is possible since the aforementioned probability functions are differentiable. Differentiation and modified product rule were used to obtain the required ordinary differential equations, whose solutions are the respective probability functions. The different conditions necessary for the existence of the ODEs were obtained and it is almost in consistent with the support that defined the various probability functions considered. The parameters that defined each distribution greatly affect the nature of the ODEs obtained. This method provides new ways of classifying and approximating other probability distributions apart from Gumbel distribution considered in this chapter. In addition, the result of the quantile function can be compared with quantile approximation using the quantile mechanics.

On the Epidemiology and Statistical Analysis of HIV/AIDS Patients in the Insurgency Affected States of Nigeria

BACKGROUND: The effect of insurgencies on a nation regarding the economy, education, health and infrastructure cannot be overemphasised. AIM: This research is therefore focused on analysing the incidence of HIV/AIDS disease in states affected by the activities of the Boko Haram insurgency in Nigeria. MATERIAL AND METHODS: The data collected refer to the period from 2004 to 2017, reporting information on 16,102 patients and including the age, gender, year of diagnosing and status of the patients. Descriptive, Chi-square test of independence and Correlation analyses were performed using Statistical Package for Social Sciences (SPSS) version 20. RESULTS: It was discovered that the majority of those living with HIV/AIDS in these Boko Haram ravaged areas are females between the age group of 30 years to 39 years. Reported cases of HIV/AIDS started increasing significantly from age 20, and the highest number of reported cases of HIV/AIDS was recorded in the year 2017. CONCLUSION: The status of the patient was found to be dependent on both the gender and age of the patients’ treatment, though the strength of the linear relationship between status and age is not significantly different from zero.

Survey dataset on the types, prevalence and causes of deviant behavior among secondary school adolescents in some selected schools in Benin City, Edo State, Nigeria

This data article contains the exploratory analysis of data obtained from a field survey done to determine the types, prevalence and likely causes of deviant behaviors among secondary schools’ adolescents in some selected schools in Benin City. The data presents the findings in tables and will be helpful in childcare guidance, counseling, education management and for education policy makers.

Statistical data analysis of cancer incidences in insurgency affected states in Nigeria

This article provides details about the various cancer types recorded in Northeastern states of Nigeria currently being affected by insurgency in Nigeria. The dataset was described and chi-square test was used to determine the dependency of the variables under consideration on each other. Also, linear, logarithmic, inverse, quadratic, cubic, power, growth, exponential and logistic regression models were fitted to the dataset to show the relationship between them.

Semi-analytical Methods for Higher Order Boundary Value Problems

This work considers the solution of higher order boundary value problems using Homotopy perturbation method (HPM) and modified Adomian decomposition method (MADM). HPM is applied without any transformation or calculation of Adomian polynomials. The differential equations are transformed into an infinite number of simple problems without necessarily using the perturbation techniques. Two numerical examples are solved to illustrate the method and the results are compared with the exact and MADM solutions. The accuracy, simplicity and rapid convergence of HPM in handling the boundary value problems reveals its advantage over MADM.

Natural Frequencies of an Euler-Bernoulli Beam with Special Attention to the Higher Modes via Variational Iteration Method

In this chapter, natural frequencies of an Euler-Bernoulli prismatic beam on different supports are analyzed. The variational iteration method (VIM) is employed to compute the said natural frequencies especially for the higher modes of vibration. Some numerical examples are presented with the view to demonstrating excellent agreement between the results obtained using VIM and other methods.