Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 3Rama Shanker, Kamlesh Kumar Shukla, Tekie Asehun LeonidaA two-parameter Poisson-Sujatha distribution which is a Poisson mixture of two-parameter Sujatha distribution, and includes Poisson-Sujatha distribution as particular case has been proposed. Its moments and moments based measures including coefficient of variation, skewness, kurtosis and index of dispersion have been obtained. Maximum likelihood estimation has been explained for estimating its parameters. Goodness of fit of the proposed distribution has been explained with two over-dispersed count datasets and the fit has been compared with one parameter Poisson-Lindley distribution and Poisson-Sujatha distribution and a generalization of Poisson-Sujatha distribution.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 3Robert Kay Ankomah, Emmanuel Kojo Amoah, Elvis Agyei ObengFormative outcomes and terminal scores of association football serves as the basis for most placed bets in Ghana. These formative outcomes and terminal scores are largely dependent on the quality of teams’ performance as against that of the opponent(s). The paper proposes a predictive model that assesses the quality of teams’ performance via teams’ scoring intensity by encapsulating Foul for teams (FoulF), Fouls against the team (FoulA), Red cards against the team (Red CA), Corners profile for the team (CornP), Yellow cards against the team (YelCA) and Shots on targets (ShotT) of home and away teams, and further used these scores’ intensities between any two teams to calculate the probabilities of win, draw or lose between teams using bivariate Poisson distribution. The paper concludes that, the higher the scoring potency of teams, the higher their probability of winning and vice-versa. The paper also avers that, on average there appears not to be any “wild” difference in playing at home or away contrary to conclusions drawn by previous researchers in playing at home without skills dominance of the home team. Both home and away scores are influenced by corner profiles and shots on targets of teams.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 2Essam El-Seidy, Maan T. Alabdullah, Shahd H. AlkarazInitially, we provide basic knowledge of definitions and concepts related to the concept of matching in the graph. We are studying a model of games based on two players who take turns adding edges to this process eventually produces a maximal matching of the graph. We call the first Maximizer and second player Minimizer. The first aims to get a final matching to be large while the second one wants to reduce it. Maximizer wins if he manages a maximal matching while Minimizer wins if he can prevent him from doing this. The matcher number is the number of edges chosen when both players play optimally, while the matching number is the number of maximum matching edges. In this research we study the relationship between and . And we also prove some results on types of graph.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 2Onyekachi Akuoma Mabel, Olanrewaju Samuel OlayemiThis study aims to draw attention to the best extraction technique that may be considered when using the three of the most popular methods for choosing the number of factors/components: Principal Component Analysis (PCA), Maximum Likelihood Estimate (MLE) and Principal Axis Factor Analysis (PAFA), and compare their performance in terms of reliability and accuracy. To achieve this study objective, the analysis of the three methods was subjected to various research contexts. A Monte Carlo method was used to simulate data. It generates a number of datasets for the five statistical distribution considered in this study: The Normal, Uniform, Exponential, Laplace and Gamma distributions. The level of improvement in the estimates was related to the proportion of observed variables and the sum of the square loadings of the factors/components within the dataset and across the studied distributions. Different combinations of sample size and number of variables over the distributions were used to perform the analysis on the three analyzed methods. The generated datasets consist of 8 and 20 variables and 20 and 500 number of observations for each variable. 8 and 20 variables were chosen to represent small and large variables respectively. Also 20 and 500 sample sizes were chosen to represent also the small and large sample sizes respectively. The result of analysis, from applying the procedures on the simulated data set, confirm that PC analysis is overall most suitable, although the loadings from PCA and PAFA are rather similar and do not differ significantly, though the principal component method yielded factors that load more heavily on the variables which the factors hypothetically represent. Considering the above conclusions, it would be natural to recommend the use of PCA over other extraction methods even though PAF is somehow similar to its methods.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 2Chibuikem C. Nwagwu, Uchenna P. OgokeThe aim of this research work is to observe the changes in the population structure and distribution of Nigeria within one score years and a decade (1991 – 2020) by identifying the proportion of the Nigerian population that is women within the child-bearing age (15 – 49 years). The work uses three different population growth models – Exponential Growth Model, Hyperbolic Growth Model and a revised Exponential Growth Model – on the population data. The work compares the population distribution from 1991 to 2020 graphically for all the three growth models to see the one that best fits the data which was used to predict the population for the year 2020. Having obtained the proportion for each state, we built maps for 1991 and 2020 using ArcGIS software. The results show which states had highest number of women in child-bearing age in the different years as well as the states with the least number of women in child-bearing age. From the map, we noticed that states like Lagos, Kano and Rivers remained in the Red zone (higher population of women of child-bearing age) while the likes of FCT, Nassarawa and Yobe did not move out of the Blue zone (lower population). With the results of this research, an idea of how Nigeria’s population will be in the coming years especially in terms of the prospect of population growth, fertility, etc. can be known and planned for. Background: The varying stance of researchers on the best model to use for population projections is one of the motivations for engaging on this project. More so, we tried to access specific data on the population of women in the child-bearing age in the country but this appears not to be available. Such a critical statistical information ought to be readily available hence, we took the leap to make this valuable contribution to the body of knowledge because information on the number of women in child-bearing age is information on the possible future population. This can also be used to study other concepts like child-woman ratio and mean age of mothers. This project goes further to x-ray the cohort on a state-by-state basis using spatial representation on a map. It groups states into three zones to depict the number of cohort in the states so as to show which states fall into the different zones. Another aspect of this work is the comparative study of the number of cohort in the 1991 population against that in the 2020 projected population. Projection here is based on the best model established early in this work.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 2Osama Rashad El-GendyIn this paper, the concept of bipolar fuzzy α-ideal of BP-algebra is introduced. We introduced α-ideal and fuzzy α-ideal. Several theorems are presented in this regard. The homomorphic image and inverse image of the bipolar fuzzy α-ideal are studied.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 1K. C. N. Dozie, C. C. Ibebuogu, H. I. Mbachu, M. C. RaymondThis study presents time series analysis on a method of modeling the church marriages in time series decomposition, when trend-cycle component is linear. Empirical example was drawn from monthly records of number of church marriages in Imo State, Nigeria over the period of January, 1997 to December, 2016. The ultimate objective of this study is therefore, to determine the appropriate model of the monthly number of church marriages over the period under investigation. The method adopted is Buys-Ballot procedure developed for choice of model and choice appropriate transformation, among other uses, based on row, column and overall means and variances of the Buys-Ballot table. Result from the test shows that, the appropriate model of original data is multiplicative. The test requires that the study series satisfies the assumptions of the time series model.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 1Samuel U. Enogwe, Ben I. Oruh, Happiness O. Obiora-IlounoThis study discusses the application of replacement model in the hotel industry. The ultimate objective is to determine the replacement age for LED bulbs in hotel rooms. The method adopted considered cost of replacement of LED bulbs as random variables and utilized goodness-of-fit test to determine the probability distribution of replacement costs. The result showed that the LED bulbs burn for about 7.53 hours and about 78 bulbs failed per hour, resulting to an average individual replacement cost of about N41,600.52 per period of replacement or N12.47 per hour. In addition, it was observed that individual replacement of LED bulbs is required from period 1 (i.e., between 4381 and 8760 hours) through period 6 (i.e., between 26281 and 30660 hours), and after period 6 (i.e., between 26281 and 30660 hours), the group replacement is implemented with a replacement cost of about N54,450.00. Consequently, the study recommended the use of individual replacement policy for the hotel under investigation over the group replacement policy.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 1Samuel Olorunfemi Adams, Muhammad Ardo BamangaThe need to have a quantitative means of modelling and predicting rainfall is very important for the purposes of Airplane movements, Agriculture, planning and policy formulation. The aim of this study is to propose a model of Seasonal Autoregressive Integrated Moving Average (SARIMA) model to model and forecast the monthly frequency of the rainfall in Abuja, Nigeria for the period 1996 to 2018. The data was obtained from Nigerian Meteorological Agency (NiMet) Abuja, Nigeria and the analysis was based on probability Seasonal time series modelling approach. The Plot of the original data shows that the time series is stationary and the Augmented Dickey-Fuller test did not suggest otherwise. The graph further displays evidence of seasonality and it was removed by seasonal differencing. The plots of the ACF and PACF show spikes at seasonal lags, the minimum Akaike information criterion (AIC) was 3618.5, Bayesian Information Criterion (BIC) was 3624.3, maximum Coefficient of Determination (R2) was 0.799 and all the parameters of the proposed SARIMA model were statistically significant at p < 0.05, suggesting SARIMA (0, 0, 2)(0, 1, 2)12 as the best for modeling and predicting the monthly rainfall in Abuja, Nigeria. The fitted model was used to make forecast for the next four proceeding years, the average predicted rainfall for the peak periods i.e. April, May, June, July, August and September for the years; 2019, 2020, 2021 and 2022 were; 335.5mm, 337.5mm, 339.3mm and 341.2mm respectively, this implies; a 3.5%, increase in rainfall from 2018 to 2019, 4.% increase in rainfall from 2018 to 2020, 4.7%, increase in rainfall from 2018 to 2021 and a 5.2%, increase in rainfall from 2018 to 2022. The results are useful for predicting the expected rainfall in Abuja in the next four years and also provide information that would be helpful for decision makers in formulating policies, planning and mitigating the problems of flooding in Abuja. Thus, the study recommends among others that Federal Government and minister of the federal capital territory, Abuja should commence the process of avoiding flood by building dikes, levees and provision of adequate drainage systems in the city.

Abstract: Publication year: 2020Source: American Journal of Mathematics and Statistics, Volume 10, Number 1Shafaq Ayub, Yasmin Zahra JafriAutoregressive Integrated Moving Average (ARIMA) has been considered a popular linear model for forecasting time series. Artiﬁcial Neural Network (ANN) has been considered a powerful tool which is used to define the complex economic relationships with various patterns. In this study, the forecasting performance of Hybrid ANN-ARIMA is compared with Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) of KSE viz. National Foods (NATF) and Engro Foods (EFOOD). Experimental results obtained show the excellence of Hybrid NN-ARIMA model over ANN and ARIMA, respectively. Further, it can be concluded that Hybrid ANN-ARIMA model has the best forecasting accuracy for forecasting stock price.