by W.M. Afify
Original Research
This paper considers the estimation problem for inverse flexible Weibull model, when the lifetimes are collected under type-II progressive interval censoring. The maximum likelihood and the Bayes estimators for the two unknown parameters of the inverse flexible Weibull distribution are derived. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. Bayesian estimation for population parameter under type-II progressive interval censoring is studied via Markov Chain Monte Carlo (MCMC) simulation. To illustrate the proposed methods will discuss an example with the real data. Finally, comparing the two techniques through comparisons between the maximum likelihood using Monte Carlo simulation and bootstrap method on the one hand, and comparing them with the Bayes estimators using MCMC study on the other hand.
American Journal of Applied Mathematics and Statistics. 2016, 4(4), 126-135. DOI: 10.12691/ajams-4-4-5
Pub. Date: September 01, 2016
21402 Views4710 Downloads
by B.O. EKPENYONG
Original Research
Divergently different time series are considered in this article. The monthly passengers traffic at Cross lines limited, Calabar from 1990 to 2015 and monthly incidence of tuberculosis diseases at University of Calabar Teaching Hospital based from 1990-2015. The research adopted the statistical models based on time series analysis by Box and Jenkins methodology via the autocorrelation and the partial autocorrelation functions which showed that the two series are not stationary. Logarithm transformation was used to stabilize the variances of the two series and the residual autocorrelation and the partial autocorrelation functions is made stationary. Both regular and seasonal differencing was applied to the two-transformed set of data to obtain stationary series. The study employed ARIMA model on the classes of the two series, and the parameters of the identified model were estimated by the use of SPSS. The two models so chosen were ARMA (2,1,0) x (1,1,1)12 for passengers’ traffic and ARMA (1,0,1) x (1,1,2)12 for tuberculosis cases and forecasts was done for 12 months for the two series. The adequacy of the model was achieved and model fit for passengers traffic yields R-square, RMSE and MAPE of 0.876, 9.137, and 27.479 respectively and for tuberculosis cases yields R-square, RMSE and MAPE of 0.614, 6.785 and 26.522 respectively, recommendation and conclusion was made for the area of study.
American Journal of Applied Mathematics and Statistics. 2016, 4(4), 118-125. DOI: 10.12691/ajams-4-4-4
Pub. Date: August 22, 2016
12667 Views2960 Downloads
by T. Mayooran and Elliott Light
Original Research
Solving a system of equations by Ax=b, where A is a nn matrix and b and n1 vector, can sometime be a daunting task because solving for x can be difficult. If you were given an algorithm that was efficient, that’s great! What if you could make it solve the problem even faster? That’s even better. We will first take a look at establishing the basics of the successive over-relaxation method (SOR for short), then we’ll look at a real-world problem we applied the SOR method to, solving the heat-equation when a constant boundary temperature is applied to a flat plate.
American Journal of Applied Mathematics and Statistics. 2016, 4(4), 113-117. DOI: 10.12691/ajams-4-4-3
Pub. Date: August 13, 2016
12983 Views3055 Downloads1 Likes
by Olusegun Adelodun
Original Research
Mathematics is a very important subject. It is the language of science and technology and so it is a force to reckon with in the development of any nation. Several studies on factors that affect mathematics achievement have been conducted. However, studies on factors that affect mathematics achievement among Polytechnics students in Nigeria seem to be rare. This study identified the variables that tend to affect academic performance among mathematics students and developed covariance structure model for examining the relationships between the variables. This was with a view to providing an appropriate frame work for predicting academic performance. Study participants were 240 students selected by convenience sampling from six Polytechnics (three State-owned and three Federal-owned) in the South-Western Nigeria. A self-report questionnaire was administered on participants to collect information on demographic factors, self concept, training environment and circumstances used to determine the academic performance of students. Data collected was analyzed using percentages and covariance structure model technique. It explained self-concept, training environment and circumstances affect academic performance, with a good model fit. The model supposes that the perceived attributes of self concept, training environment and circumstances in polytechnics predict the academic performance. The result showed that self-concept, training environment and circumstances has influences on students’ academic performance in Nigerian polytechnic.
American Journal of Applied Mathematics and Statistics. 2016, 4(4), 108-112. DOI: 10.12691/ajams-4-4-2
Pub. Date: July 21, 2016
14895 Views3833 Downloads
by Ophir Nave
Original Research
In this study, we investigate the problem of the effects of droplets dispersion dynamics on ignition of polydisperse spray in turbulent mixing layers using probability density function. Studies of this problem have been found to be instrumental in developing understanding of turbulent combustion including the ignition of turbulent gaseous diffusion flames. The parameters used to describe the distribution of droplet sizes are the moments of the droplet size distribution function which are allowed to vary in the fourth vector (x,y,z,t). In our analysis we applied the Homotopy Analysis Method. This method contains a certain auxiliary parameter which provides a way to control the convergence region and the rate of convergence of the series solutions.
American Journal of Applied Mathematics and Statistics. 2016, 4(4), 99-107. DOI: 10.12691/ajams-4-4-1
Pub. Date: July 11, 2016
14913 Views4576 Downloads