Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication.

The use of quantile functions of probability distributions whose cumulative distribution is intractable is often limited in Monte Carlo simulation, modeling, and random number generation. Gamma distribution is one of such distributions, and that has placed limitations on the use of gamma distribution in modeling fading channels and systems described by the gamma distribution. This is due to the inability to find a suitable closed-form expression for the inverse cumulative distribution function, commonly known as the quantile function (QF). This paper adopted the Quantile mechanics approach to transform the probability density function of the gamma distribution to second-order nonlinear ordinary differential equations (ODEs) whose solution leads to quantile approximation. Closed-form expressions, although complex of the QF, were obtained from the solution of the ODEs for degrees of freedom from one to five. The cases where the degree of freedom is not an integer were obtained, which yielded values closed to the R software values via Monte Carlo simulation. This paper provides an alternative for simulating gamma random variables when the degree of freedom is not an integer. The results obtained are fast, computationally efficient and compare favorably with the machine (R software) values using absolute error and Kullback-Leibler divergence as performance metrics.

Hepatitis E Infection in Nigeria: A Systematic Review.

BACKGROUND: Research done globally on hepatitis E virus (HEV) infection is far fewer compared with other types of hepatitis virus infection. Little is known on the prevalence of HEV in Nigeria. AIM: The present study presents the prevalence of HEV infection in Nigeria from a few available research papers on HEV. The detailed statistical analysis was used to analyse the prevalence of HEV in humans and animals. MATERIAL AND METHODS: A literature search in Web of Science, Scopus and PubMed databases was done, and a final 7 articles were selected. Minitab 17.0 was used to perform the correlational and binary logistic analyses. RESULTS: Serum and faecal analysis of blood and stool samples of 1178 humans and 210 pigs (animals) were done, and the presence of anti-HEV IgG or HEV RNA in the study samples were 127 and 138 respectively. Further analysis showed the prevalence of HEV are 10.8% and 65.7% in humans and animals, respectively. Weak positive non-significant association (r = 0.327, p-value = 0.474) was obtained between the target (humans and animal) and the HEV infection (positive) groups. The application of binary logistic regression yielded an equation that can be used to predict the target group from the HEV positive humans or animals. Generally, the logistic model was not statistically significant (p-value = 0.376), and the model was able to explain 9.3% of the deviation or variability of the model. The odds ratio is OR = 1.0344 with 0.9550, 1.204 95% Confidence Interval (CI). Thus, in Nigeria, the odds of prevalence of HEV in animals are 1.0344 higher than humans. CONCLUSION: The risk factors obtained from the few available articles are consistent with the global epidemiology of HEV infection. Food and animal handlers and those that consume unsafe water are the key people at risk of HEV infection in Nigeria.

Survival Analysis of Cancer Patients in North Eastern Nigeria from 2004 - 2017 - A Kaplan - Meier Method.

BACKGROUND: Cancer is a deadly malignant disease and is prevalent in Sub Saharan Africa. The North East part of Nigeria in particular and the country, in general, are struggling to cope with the increasing burden of cancer and other communicable and non-communicable diseases. The situation is worsened by the ongoing insurgency and terrorist activities in the area. AIM: The aim of this paper is to present the research findings from a cohort study aimed at the analysis of the estimation of the survivorship time of the real data of cancer patients in the North-eastern part of Nigeria and to establish if the insurgency in the region has contributed negatively to the life expectancy of its inhabitants. MATERIAL AND METHODS: The record of 1,090 patients from medical records departments of the University of Maiduguri Teaching Hospital (UMTH), located in Maiduguri, the capital city of Borno State in northeast Nigeria was obtained. The record showed patients that were diagnosed and died of one type of cancer or the other from 2004 to 2017. All the cancer cases included in the present study were grouped into sex, age, marital status, occupation, date admitted and date of death/discharge. Descriptive statistics and Kaplan-Meier method were used to analyse the data using SPSS version 23 while Microsoft EXCEL and Minitab 16.0 were used for data cleansing and organisation. RESULTS: Of the 1,090 patients analysed, 920 (84.40%) experienced the event, i.e. death, while 170 (15.60%) patients were censored. The data were analysed based on the ages and sex of the patients. 50.20% of the patients were of ages 21-50 years. The proportions of patients in this age bracket surviving past 7 days are 75%, while those between ages 80 years and above is 12 days. Others are of survival time of 5 days (ages 0-20 years) and 7 days (51-79 years). Using sex, 75% of the patients' survival time is 7 days in the case of male and 6 days for females. It is safe to say that the survival time for cancer patients of the university the Maiduguri is 6 days and the result reflects the Northeastern part of Nigeria. This is because the hospital is one of few tertiary healthcare facilities in that area and consequently, cancer cases are often referred there. CONCLUSION: Cancer incidence is high, and the probability of survival reduces as the survival time increases. This is a dire situation in need of urgent intervention from the government, groups and individuals to tackle the scourge of cancer, thereby improving on the life expectancy battered by the ongoing Boko Haram insurgency in that region.

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.

Data in support of high rate of pregnancy related deaths in Maiduguri, Borno State, Northeast Nigeria.

Pregnancy related deaths (PRD) are public health concern in most developing countries and Nigeria in particular. Despite the efforts put in by the concerned authorities, PRD remains an integral part of maternal mortality or maternal deaths in Nigeria in general and Borno state in particular, as evidenced from the records obtained from Umaru Shehu Hospital, Maiduguri (a state hospital in the state capital. The data contains frequency of PRD in months and grouped into gynaecology, ante-natal and post-natal, and labour obtained from mid-2009 to mid - 2017. The statistical analysis of the data may reveal the extent of incidence or epidemiology of PRD is in the state.

Datasets on the statistical properties of the first 3000 squared positive integers.

The data in this article are as a result of a quest to uncover alternative research routes of deepening researchers' understanding of integers apart from the traditional number theory approach. Hence, the article contains the statistical properties of the digits sum of the first 3000 squared positive integers. The data describes the various statistical tools applied to reveal different statistical and random nature of the digits sum of the first 3000 squared positive integers. Digits sum here implies the sum of all the digits that make up the individual integer.

Personal name in Igbo Culture: A dataset on randomly selected personal names and their statistical analysis.

This data article contains the statistical analysis of Igbo personal names and a sample of randomly selected of such names. This was presented as the following: 1). A simple random sampling of some Igbo personal names and their respective gender associated with each name. 2). The distribution of the vowels, consonants and letters of alphabets of the personal names. 3). The distribution of name length. 4). The distribution of initial and terminal letters of Igbo personal names. The significance of the data was discussed.

Datasets on the statistical and algebraic properties of primitive Pythagorean triples.

The data in this article was obtained from the algebraic and statistical analysis of the first 331 primitive Pythagorean triples. The ordered sample is a subset of the larger Pythagorean triples. A primitive Pythagorean triple consists of three integers a, b and c such that; [Formula: see text]. A primitive Pythagorean triple is one which the greatest common divisor (gcd), that is; [Formula: see text] or a, b and c are coprime, and pairwise coprime. The dataset describe the various algebraic and statistical manipulations of the integers a, b and c that constitute the primitive Pythagorean triples. The correlation between the integers at each analysis was included. The data analysis of the non-normal nature of the integers was also included in this article. The data is open to criticism, adaptation and detailed extended analysis.

Exploration of UK Lotto results classified into two periods.

United Kingdom Lotto results are obtained from urn containing some numbers of which six winning numbers and one bonus are drawn at each draw event. There is always a need from prospective players for analysis that can aid them in increasing their chances of winning. In this paper, historical data of the United Kingdom Lotto results were grouped into two periods (19/11/1994-7/10/2015 and 10/10/2015-10/5/2017). The classification was as a result of increase of the lotto numbers from 49 to 59. Exploratory statistical and mathematical tools were used to obtain new patterns of winning numbers. The data can provide insights on the random nature and distribution of the winning numbers and help prospective players in increasing their chances of winning the lotto.