Rainfall is the natural source of water, it has greater impact on agricultural activities and domestic consumptions. Since Meru and Embu regions are agricultural zones relying heavily on rainfed agriculture, it is important for farmers to know rainfall patterns prevailing in their regions.In this study we model rainfall patterns in Meru and Embu regions of Kenya using Monthly and yearly rainfall data. ARIMA model was developed using Box-Jenkins (BJ) Methodology and fit to monthly and yearly average amount of rainfall. The data were examined to check for the most appropriate class of ARIMA processes. This was done by selecting the order of the consecutive and seasonal differencing. The auto-correlation function (ACF) and the partial autocorrelation function (PACF) are the most important elements of time series analysis. Using the AIC criterion ARIMA (1,1,1)(0,1,1) 12 was identified as the best model . This model was used to forecast monthly rainfall patterns for five years and found that future rainfall patterns will change with time as contributed by many factors. It was recommended that, future researchers should consider zoning regions, identify other factors contributing to change in rainfall patterns and apply developed Arima model. Keywords: ARIMA model, Box-Jenkins methodology, forecasting, seasonal differencing.
An optimal measure of performance is the one that lead to maximization of average error rate or probability of misclassification. This paper aimed to compare between the maximum likelihood rule and logistic discriminant analysis in the classification of mixture of discrete and continuous variables. The efficiency of the methods was tested using simulated and real dataset. The result obtained showed that the maximum likelihood rule performed better than the logistic discriminant analyses, in maximizing the average error rate in both experiment conducted. Keyword: Maximum likelihood rule, Logistic discriminants, error rate, Likelihood ratio, Discriminant analysis.
This paper investigates a batch arrival queueing system in which customers arrives at the system in a Poisson stream following a compound Poisson process and the system has a single server providing three types of general heterogeneous services. At the beginning of each service, a customer is allowed to choose any one of the three services and as soon as a service of any type gets completed, the server may take a vacation or may continue staying in the system. The vacation time is assumed to follow a general (arbitrary) distribution and the server vacation is based on Bernoulli schedule under a single vacation policy. During the server vacation period, impatient customers are assumed to balk. This paper described the model as a bivariate Markov chain and employed the supplementary variable technique to find closed-form solutions of the steady state probability generating function of number of customers, the steady state probabilities of various states of the system, the average queue size, the average system size, and the average waiting time in the queue as well as the average waiting time in the system. Further, some interesting special cases of the model are also derived. Keywords Batch Arrivals. Queueing System. Balking. Heterogeneous types of Service. Bernoulli schedule server vacation. Bivariate Markov Processes. MSC2020-Mathematics Subject Classification 34B07, 60G05, 62E15
The Fractional Calculus is the theory of integrals and derivatives of arbitrary order which unifies and generalizes the concepts of integer-order differentiation and n-fold integration. Time fractional partial differential equation is one of the topics in the analysis of fractional calculus theory which can be obtained from the standard partial differential equations by replacing the integer order time derivative by a fractional derivative. In this study a recent and reliable method, namely the reduced differential transform method which is introduced recently by Keskin and Oturanc (Keskin Y. and Oturan G. 2009, 2010)was applied to find analytical solutions of one dimensional time-fractional Airy’s and Airy’s type partial differential equations subjected to initial condition. The fractional derivative involved here is in the sense of Caputo definition, for its advantage that the initial conditions for fractional differential equations take the traditional form as for integer-order differential equations. In order to show the reliability of the solutions examples are constructed and 3D figures for some of the solutions are also depicted. Keywords: One dimensional; Time-fractional
Solar energy is a renewable resource, clean and ecologically friendly. Solar thermal energy is attractive alternative energy to drive the adsorption of refrigeration machines. This work presents a numerical investigation of the effect of climatic governing parameters such as ambient temperature and component temperatures on the performance of solar adsorption refrigeration systems using methanol/activated charcoal pairs. Activated carbon as adsorbent and methanol as a refrigerant is selected. Some predictive empirical equations accounting for heat balance in the solar collector components, instantaneous heat and mass transfer in adsorbent bed, and performance parameters were presented. Interactive C++ programming was developed to carry out the parametric study of some climatic factors such as ambient temperature and solar radiation intensity with aperture width of 0.14 m, collector length of 2.1m on the system performance. The effect of ambient temperature and component temperatures with aperture width, collector length, on specific cooling power (SCP), refrigeration cycle COP (COP cycle ), and solar coefficient of performance (COPs) are being investigated. The results are presented in form of profiles such as pressure developed in the generator, specific cooling power and system coefficient of performance profiles, under varying weather conditions and ambient temperature, operating conditions of evaporating temperature, T ev = 0 o C, condensing temperature, T con = 30 o C and desorption temperature of 100 o C, The influences of operating and design parameters on the system performance are significant. The system performance shows no appreciable changes with varying condenser temperature with significant effect with varying evaporation and desorption temperature. It is shown clearly that for different desorption temperatures below 120 o C there is an appreciable effect on the system performance parameters. The study has revealed the system attains a promising performance of the adsorption refrigeration system using AC / methanol pair driven by solar energy. Keywords : Adsorption; Refrigeration; Activated carbon/methanol; Simulation
The best classification rule is the one that leads to the smallest probability of misclassification which is called the error rate. This work focused on three classification rules for mixture of discrete and continuous variables with the aim to evaluate the performance of these rules to in classification of individuals into several categories. Applications were done using simulated data and real life data. The result obtained revealed that the location model achieved better result than the other two rules in minimizing the average error rate in both datasets. Keyword: Location Model, Linear Discriminant Models, Quadratic, Discriminant Model, Error Rate.
The concept of length biased distribution can be employed in development of proper models for life time data. Its method is adjusting the original probability density function from real data and the expectation of those data. This adjustment can bring about correct conclusions on the models. In this research, a new class of length biased approach was introduced to gumbel distribution which is called length baised gumbel distribution (LBGD). The theoretical properties of this distribution were derived and the model parameters were also estimated by Maximum Likelihood Estimation (MLE). This procedure is to adjust the original probability density function from real and ex-pected data which leads to good conclusion on the model. This distribution was later applied to wind speed data (extreme value data). Keywords: Extreme Value Theory, Weighted Distribution, Length biased Gumbel Distribution, Alkaine Information Criterion, Wald Test
In this article, we proposed a new distribution known as the Exponentiated Inverse Power Pranav distribution for modeling lifetime data sets with monotone and non-monotone shapes in their hazard rates. Along with some of the basic properties, we however, studied the maximum likelihood estimation of the parameters of the proposed distribution. The model was subjected to life application with a dataset and compared to other sub-models. The new distribution was found to have a best fit more than the competing sub-models. Keywords: Pranav distribution, Inverse Power Pranav distribution, Exponentiated distributions, Maximum Likelihood estimation, Exponentiated Inverse Power Pranav distribution
This study investigated the interaction effect of meta-cognitive strategy on mathematical disposition and problem-solving ability. This is a quasi-experimental study with 2 x 2 factor design. The subjects of this study were 138 students of 8th grade in Islamic Junior High School in Jombang, Indonesia which is divided into two groups i.e. control class and experiment class. There were 69 students in the experimental group with metacognitive strategy and 69 students in the control group with conventional strategy. Data were collected through mathematics questions test and mathematical disposition questionnaire. The mathematical disposition questionnaire was used to determine the students' mathematical disposition abilities. The data were analysed using analysis of variance. The study reports that there is no significant interaction effect of metacognitive strategy on the mathematical disposition and problem-solving ability. Keywords- Meta-cognitive Strategy, Mathematical Disposition, Problem-Solving Ability
This research work investigated a Poisson regression model that fit the average number of carryover a student will have and factors affecting average number of students carryover such as cumulative grade point average (CGPA), Sex, Age, Marital status (Single and Married), Residence (Inside the campus and outside the campus), Choice of course of study, Jamb Mathematics score and Relationships (dating or not dating). Data on average number of carryover for students used in this work were collected from Department of Statistics, Michael Okpara University of Agriculture, Umudike while data on other factors were collected primarily by use of questionnaires. Poisson log-linear regression model was used to fit the data collected. It was discovered that students living inside campus have lesser number of carryover than students living off campus and also it was observed that students who are married have greater number of carryover than those who are not. The number of student’s CGPA inside campus is greater than those students who live off campus. From the analysis obtained, we found out that the factors; CGPA, Marital status and Residence were the major contributors to the number of carryover for the students of statistics Department Michael Okpara University of Agriculture, Umudike. Keywords: Poisson Regression, cumulative grade point average (CGPA), Age, Sex, Marital status, residence and relationships.
The impact of transport connectivity and infrastructure on trade and overall economic development in the West African region cannot be over emphasized. Generally, it has been established that poor transportation systems have negative knock-on effects on the economies of countries. Thus, this study identifies and discussed the barriers and facilitators regarding transport connectivity，performance of trade and overall economic development of member countries of the ECOWAS region. We develop a gravity model to assess the impact of transport connectivity and infrastructure on bilateral and intra-regional trade across the study region. Also, multilateral trade resistance (MTR) terms are included in the modelling structure as a variable to capture the comparative trade cost between transacting partner economies. The outcome of the analysis indicates a positive connection between transport connectivity and infrastructure along with international and intra-regional trade. This implies that transport connectivity and infrastructure impact the overall growth and performance of trade in the ECOWAS region and the level of impact is statistically significant. The analysis show that including a rail connection between trading country partners in the study area will result in an average upsurge of trade performance by 3.5 per cent. Similarly, the results also prove that a 10 per cent decrease in the distance of sea and air upsurges trade by 0.52 per cent and 0.31 per cent, respectively. Likewise, improving the rail and road density of the trading partner countries ranked as the second factor that contributes greatly to improving trade performance in the study area. Similarly, the performance of logistics (such as LPI) indicates a substantial and comparatively robust impact on the flow of international and intra-regional trades. Key words: ECOWAS, MTR, LPI, LSCI, transport connectivity, transport infrastructure, gravity model
In this study, a new distribution known as the Exponentiated Rama distribution has been proposed. The aim was to generalize the one parameter Rama distribution using the exponentiation technique. Some properties of proposed distribution are derived. The maximum likelihood method was used for the estimation of model parameters. The proposed distribution was subjected to real life application using a set of lifetime data and compared to Rama distribution, Exponentiated Akash distribution and Exponentiated Exponential distribution and it was found to provide the best fit than other competing distributions. Keywords: Rama distribution, Exponentiated distributions, Order statistics, Moments
Let be a quiver, any field, and denotes the path algebra of with coefficients in . A module is called hereditary if all its submodules are projective. In this paper, we characterize hereditary modules over the path algebra of a quiver which contains cycles. Keywords: path algebras, representations of quivers, hereditary modules
Sexually Transmitted diseases are major problems in the health sector. Several researches have shown that it can shorten the lives of people and can cause serious morbidity. This research examined application of Chi Square Statistic and linear logistic regression model to predict the chances of survival among victims of Urinary Tract Infection and Gonorrhoea based on their age, gender and the disease type in Ondo State, Nigeria. Based on the data analysed, we were able to deduce that the male gender irrespective of the age has a greater chance of surviving any sexually transmitted disease. It is therefore recommended that the female sex irrespective of their age undergo constant examination for early detection of any sexually transmitted disease. It is also recommended that there should be sensitization programme for female on sex education irrespective of their age to enable them avoid the infection. Keywords : Sexually Transmitted Disease, Logistic Regression, Odd Ratio, Urinary Tract Infection and Gonorrhoea.
An insurance system is a mechanism for reducing the adverse financial impact of random events that prevents the fulfillment of reasonable expectations, i.e. Insurance is designed to protect against serious financial reversals that may result from random events intruding on the plans of individuals. The Life Insurance Company calculates the policy price with the intent to recover claims to be paid and administrative costs and to make a profit. The cost of insurance is determined using the Mortality Table calculated by Actuaries. The insurance companies receive premiums from the policy owner and invest them to create a pool of money from which to pay claims and finance the insurance company’s operations. Rates charged for life insurance increase with the insured’s age because statistically people are more likely to die as they get older. In this paper, we have discussed different types of insurance policies including expenses and its impacts on lives. We also discussed the annual premium rates of endowment plans, three-payment plans and six-payment plans. Matlab programming is used to calculate the premium rates.
Coronavirus disease 2019 originated from Wuhan, China and spread rapidly across the globe. The virus was first identified in Nigeria on 27 th February, 2020 and announced by the Minister of Health on 28 th February, 2020 through a press briefing. As at 4 th May, 2020, the Nigeria Centre for Disease Control recorded a total of 2,802 confirmed cases of COVID-19 individuals with 93 fatalities. Available data from inception to 4 th May, 2020 were extracted from Nigeria Centre for Disease Control (NCDC) situation reports and used to trace the epidemic curves of COVID-19 in Nigeria. Furthermore, the disease transmission rate and the basic reproduction number were estimated by using an SEIHR epidemic model with the influence of awareness and medical assistance through MATLAB application. The results of the numerical evaluation of the model indicated that awareness dissemination aid in reducing the spread of COVID-19 and medical assistance has significant impact. The disease transmission rate and the basic reproduction number were estimated as and respectively. While the analysis predicted that the epidemic peak of COVID-19 in Nigeria will occur approximately 216 days from the inception of NCDC situation report. The overall outcome of the analysis advocates for more awareness campaign, accessible medical assistance and proper enforcement of adherence to strict measures for the control and possibly elimination of COVID-19. Keywords: COVID-19, Nigeria, Model, Basic reproduction number, Epidemic peak
The paper depicts assessment of the Bayesian methodology utilizing Gaussian quadrature formulas and Markov Chain Monte Carlo of the Gompertz distribution based on type I censored data with two loss functions, the Square Error loss function and the Linear Exponential loss function. In Markov Chain Monte Carlo, the full conditional distributions for the scale and shape parameters, survival and hazard functions are acquired by means Gibbs sampling and Metropolis- Hastings algorithm. The strategies for the Bayesian methodology are contrasted with maximum likelihood estimation regarding the Mean Square Error (MSE) to decide the best assessing of the scale and shape parameters, survival and hazard functions of the Gompertz distribution based on type I censored data. Keywords: Gompertz distribution, Bayesian estimation, Type I censored data, Gaussian Quadrature Formulas, Markov Chain Monte Carlo.
The majority of real-world systems within the Engineering domain and particularly the construction sector, generate enormous amounts of data every instance of time that they are in operation. This data can be collected from these systems real-time or otherwise using traditional methods or using contemporary techniques such as those that facilitate the implementation of concepts such as the Internet Of Things (IOT). Once gathered into a repository, this data can be utilized for planning, predictive, diagnostic, and other purposes. For this data to be put to such meaningful uses, there are analytics that need to be performed. This paper showcases typical examples of such analytics that generate information that can serve as decision support in a practical setting. First, background information that is necessary to support simple to complex data analytics is presented. This is followed by a case study used to demonstrate how analytics can be performed on data from an offsite concrete block production operation to gain insights into the operation and for diagnostic purposes. To achieve this, probability distributions fit to collected data for each state variable are utilized in a setup Monte Carlo simulation experiment configured to predict concrete production cycle lengths. Keywords: Data, Analytics, Offsite, Concrete block, Production, Cycle Length, Monte Carlo Simulation
In this paper we consider a mathematical model of mosquito and insecticide. The aim of this model is to reduce the amount of mosquitoes in the ponds and swamps. Mosquitos are the main cause of malaria disease. We used the optimal spray strategies to minimize the amount of mosquito, we work optimal control framework by applying the Pontryagin's Maximum Principle. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by using MATLAB.
In this study, a new four parameter distribution called the Lehmann type II generalized half logistic distribution was derived. The statistical properties of the Lehmann type II generalized half logistic distribution were studied. Estimates of the parameters of the new distribution under complete and censored observations would be obtained using the maximum likelihood estimation method. Simulation studies were carried out to assess the consistency of the maximum likelihood estimates. Application of the new distribution to a data showed that it performed better than the type I generalized half logistic distribution Keywords: distribution, censored, estimates, parameters, function, observation, Lehmann type II.
