American Journal of Applied Mathematics and Statistics

In an earlier work, recently published in this journal, we have used the Triangular Fuzzy Numbers (TFNs) as an assessment tool of student skills. This approach led to an approximate linguistic characterization of the students’ overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since two TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice.

American Journal of Applied Mathematics and Statistics. 2015, 3(5), 206-210. DOI: 10.12691/ajams-3-5-5
Pub. Date: October 20, 2015

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Imputation of Missing Values for Pure Bilinear Time Series Models with Normally Distributed Innovations

by Poti Owili Abaja, Dankit Nassiuma and Luke Orawo

Original Research

In this study, estimates of missing values for bilinear time series models with normally distributed innovations were derived by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for different pure bilinear time series models using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values. Further, the optimal linear estimates were equivalent to one step-ahead forecast of the missing value. The study recommends OLE estimates for estimating missing values for pure bilinear time series data with normally distributed innovations.

American Journal of Applied Mathematics and Statistics. 2015, 3(5), 199-205. DOI: 10.12691/ajams-3-5-4
Pub. Date: October 20, 2015

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Bivariate Test for Testing the EQUALITY of the Average Areas under Correlated Receiver Operating Characteristic Curves (Test for Comparing of AUC’s of Correlated ROC Curves)

by D. M. Senaratna, M.R. Sooriyarachchim and N. Meyen

Original Research

Methodology developed for comparing correlated ROC curves are mainly based on nonparametric methods. These nonparametric methods have several disadvantages. In this paper the authors propose an asymptotic bivariate test for comparing pairs of AUCs for independent data based on the Dorfman and Alf maximum likelihood approach. The properties of the test are examined by using simulation studies. The method is illustrated on an example of angiogram results from Sri Lanka. The test applied to the example found that there was a significant difference in the predictive power of three different cut-offs examined.

American Journal of Applied Mathematics and Statistics. 2015, 3(5), 190-198. DOI: 10.12691/ajams-3-5-3
Pub. Date: October 15, 2015

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The Moment Approximation of the First–Passage Time for the Birth–Death Diffusion Process with Immigraton to a Moving Linear Barrier

by Basel M. Al-Eideh

Original Research

Today, the the development of a mathematical models for population growth of great importance in many fields. The growth and decline of real populations can in many cases be well approximated by the solutions of a stochastic differential equations. However, there are many solutions in which the essentially random nature of population growth should be taken into account. In this paper, we approximating the moments of the first – passage time for the birth and death diffusion process with immigration to a moving linear barriers. This was done by approximating the differential equations by an equivalent difference equations. A simulation study is considered and applied to some values of parameters which showed the capability of the technique.

American Journal of Applied Mathematics and Statistics. 2015, 3(5), 184-189. DOI: 10.12691/ajams-3-5-2
Pub. Date: September 20, 2015

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Modelling the Association of Maternal Factors on Exclusive Breastfeeding among Ghanaian women Using Logistic Regression and Bootstrapping Techniques

by Michael Ofori Fosu, Kwasi Awuah-Werekoh and N.N.N Nsowah-Nuamah

Original Research

This study examines the prevalence of exclusive breastfeeding among Ghanaian women and the determining factors associated with it. The study used a data set based on a longitudinal study from the fourth round of the Multiple Indicators Cluster Survey (MICS). This was a national survey conducted by Ghana Statistical Service (GSS) in 2011 to monitor progress of women and children. A sample of 10,963 women within the reproductive age (15 – 49) years across the country between 2009 and 2011 were selected for the survey. In this study, a multiple logistic regression and bootstrap techniques were used to determine the relationship of household/maternal factors and exclusive breastfeeding among children. The estimated children who were never breastfed exclusively for the first three days of life was about 15.8% out of the 2838 women who gave birth within the survey period. This means that a lot of mothers do not practice exclusive breastfeeding in Ghana. The factors observed to be highly significantly associated with exclusive breastfeeding among Ghanaian women included ethnicity (p-value = 0.019) and antenatal care (p-value = 0.031). The results show that exclusive breastfeeding among more advantaged women are more predominant than less advantaged women. The findings further reveal that exclusive breastfeeding is more of an ethnic and regional problem in Ghana which has some cultural undertone. There is need for the government to encourage mothers’ secondary and above education. Massive public awareness and outreach programs need to include activities to fully engage community leaders and change agents on the dangers of failure to practice exclusive breastfeeding. Again, the ministry of Health should consider and come up with multifaceted program designs with clear, well-taught, understandable messages appropriate to the cultural context.

American Journal of Applied Mathematics and Statistics. 2015, 3(5), 177-183. DOI: 10.12691/ajams-3-5-1
Pub. Date: September 13, 2015

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