by S.S. Handibag, B. D. Karande and S. V. Badgire
Original Research
This paper studies the Laplace substitution method for nonlinear partial integro-differential equations involving mixed partial derivatives and further applications of same method for coupled nonlinear partial integro-differential equations involving mixed partial derivatives.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 272-280. DOI: 10.12691/ajams-6-6-9
Pub. Date: December 19, 2018
6076 Views1451 Downloads
by Obare DM and Muraya MM
Original Research
Prediction of loan defaults is critical to financial institutions in order to minimize losses from loan non-payments. Some of the models that have been used to predict loan default include logistic regression models, linear discriminant analysis models and extreme value theory models. These models are parametric in nature thus they assume that the response being investigated takes a particular functional form. However, there is a possibility that the functional form used to estimate the response is very different from the actual functional form of the response. In such a case, the resulting model will be inaccurate. Support vector machine is non-parametric and does not take any prior assumption of the functional form of the data. The purpose of this study was to compare prediction of individual loan defaults in Kenya using support vector machine and logistic regression models. The data was obtained from equity bank for the period between 2006 and 2016. A sample of 1000 loan applicants whose loans had been approved was used. The variables considered were credit history, purpose of the loan, loan amount, saving account status, employment status, gender, age, security and area of residence. The data was split into training and test data. The train data was used to train the logistic regression and support vector machine models. The study fitted logistic regression and support vector machine models. Logistic regression model showed an accuracy of 0.7727 with the train data and 0.7333 with test data. The logistic regression model showed precision of 0.8440 and 0.8244 with the train and test data. The SVM (linear kernel) model showed an accuracy of 0.8829 and 0.8612 with the train and test respectively. The SVM (linear kernel) showed a precision of 0.8785 with the train data and 0.7831 with the test data. The results showed that support vector machine model performed better than logistic regression model. The study recommended the use of support vector machines in loan default prediction in financial institutions.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 266-271. DOI: 10.12691/ajams-6-6-8
Pub. Date: December 14, 2018
9135 Views1537 Downloads1 Likes
by Fatma D.M. Abdallah
Original Research
This paper aims to explain and apply an important statistical method used for modelling categorical outcome variable with at least two unordered categories. Logistic regression model especially multinomial logistic type (MNL) model is the best choice to model unordered qualitative data. A simulation study was done to examine the efficiency of the model in representing categorical response variable. Three explanatory variables (age, species, and sex) are used for discrimination. While the outcome variable was Rose Bengal Plate Test (RBPT) results which has four outcome categories (negative, positive, false positive, and false negative). Therefore, logit model will be utilized to model this data. MNL models were fitted using SPSS packages and parameters estimated depending on maximum likelihood (MLE) by the Newton-Raphson algorithm. This model depends mainly on two estimates to interpret the results, they are the regression coefficient and the exponentiated coefficients which known as the odds ratio. This model was a good fitted for description the data of 500 values of Rose Bengal Plate Test results of Brucella in sheep and goat species. The results showed fitting of the model to the data with highly significant likelihood ratio statistic for the overall model (P value = 0.000**). Wald test was significant for all variables in positive category and this indicated that age, species and sex are good predictors for test results. The odds ratio in case of positive category for age, species and sex was 1.589, 0.214 and 0.133 respectively.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 262-265. DOI: 10.12691/ajams-6-6-7
Pub. Date: December 04, 2018
8453 Views2116 Downloads
by Michael Gr. Voskoglou
Original Research
Computational thinking is a kind of analytic thinking that synthesizes critical thinking and existing knowledge and applies them for solving complex real life and technological problems, designing systems, and understanding human behaviour, by drawing on fundamental principles of computer science. This involves frequently a degree of uncertainty and (or) the use of approximate data. On the other hand, a grey system is characterized by lack of adequate information about its components and (or) its function and the corresponding theory has found nowadays many applications to real life, science and engineering. In grey system theory the main tool for handling approximate data is the use of the grey numbers, which are indeterminate numbers defined with the help of the closed real intervals. In the present work grey numbers are used for evaluating computational thinking skills and examples are presented to illustrate our results. The outcomes of this new assessment method are compared to the corresponding outcomes of the classical method of calculating the GPA index and of a similar method developed in earlier works that uses as tools triangular fuzzy numbers instead of grey numbers.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 253-261. DOI: 10.12691/ajams-6-6-6
Pub. Date: November 30, 2018
9173 Views1815 Downloads
by Anika Tashin Khan and Hasibun Naher
Original Research
In this article the new extension of the generalized and improved (G’/G)-expansion method has been used to generate many new and abundant solitons and periodic solutions, where the nonlinear ordinary differential equation has been used as an auxiliary equation, involving many new and real parameters. We choose the Fisher Equation in order to explain the advantages and effectives of this method. The illustrated results belongs to hyperbolic functions, trigonometric functions and rational functional forms which show that the implemented method is highly effective for investigating nonlinear evolution equations in mathematical physics and engineering science.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 244-252. DOI: 10.12691/ajams-6-6-5
Pub. Date: November 14, 2018
9511 Views2249 Downloads
by Yasser M. Amer
Original Research
The weighted Laplace model is proposed following the method of Azzalini (1985). Basic properties of the distribution including moments, generating function, hazard rate function and estimation of parameters have been studied.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 239-243. DOI: 10.12691/ajams-6-6-4
Pub. Date: November 13, 2018
7062 Views1628 Downloads
by Kartik Uniyal, Girish Chandra, R.U. Khan and Y.P. Singh
Original Research
Poplar, an important tree in the agri-silvicultural system, is propagated mainly through cuttings to maintain genetic purity. Monocultures of poplar clones are amenable to many diseases as they have a narrow genetic base. Pathogenic populations have variability in terms of pathogenicity and virulence which are governed by its genetic makeup. Mapping the variability and selection of potential pathogenic isolates for breeding disease resistance remains a challenge. During the survey conducted in poplar nurseries located at different geographical sites, altogether 72 isolates of Alternaria alternata, were collected from four commercial clones of P. deltoides. Three selection methods were attempted to select fifteen potent A. alternataisolates based on growth rate, sporulation and spore size (maximum length and maximum breadth). Initially, Rough Gauging Method which is simply based upon index of sum of the character’s values and Equal Class Interval Method which depends upon the index of class interval scores were applied. To overcome the limitations of the above two methods, Unequal Class Interval Method was proposed based on Coefficient of Variation for each character assessed. The index was constructed using the geometric rather than arithmetic mean as the former normalizes the range, so that, no range dominates the scores assigned to the characters. The proposed method is recommended for the situations when the criterion variable depends upon various growth characters having inherent significant variation among each other.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 232-238. DOI: 10.12691/ajams-6-6-3
Pub. Date: November 09, 2018
9416 Views2091 Downloads
by Peter D. Hart
Original Research
Background: The five components of health-related fitness are cardiorespiratory endurance, muscular strength, muscular endurance, body composition, and flexibility. To assess an individual on all five components can be time consuming. Thus, it would be useful to fitness specialists if a simpler and valid fitness assessment was available to measure overall health-related fitness. The purpose of this study was to employ honest assessment predictive modeling to find a parsimonious set of variables that can predict overall health-related fitness. Methods: Data used for this study came from college students who completed a fitness test battery. An overall health-related fitness score (T-score) was constructed using maximal oxygen consumption (VO2, ml/kg/min), 1RM bench press (BP, lb), maximal push-up repetition (PU, #), and percent body fat (PBF, %). The set of possible predictor variables consisted of participant age (yr), sex (male/female), body mass index (BMI, kg/m2), waist circumference (WC, cm), 1RM leg press (LP, lb), countermovement vertical jump (VJ, in), flexed arm hang (FAH, sec), physical activity rating (PAR, 0 thru 10), and sit-and-reach (SNR, cm). The honest assessment predictive modeling procedure comprised three steps: 1) development of competing models using a TRAINING dataset, 2) selecting an optimal model using a separate VALIDATION dataset, and 3) assessing fitness score construct validity using a final SCORING dataset. Results: Stepwise model selection with Schwarz Bayesian criterion (SBC) on the TRAINING data resulted in five possible models including sex, VJ, PAR, and WC. Results on the VALIDATION data indicated a three-variable model had the lowest average squared error (ASE) and consisted of sex, VJ, and PAR (F=107.8, p<.001, R2=.82, SEE=3.09). Finally, predicted values from the SCORING data showed that athletes (Mean=54.9, SD=5.1) had a significantly (p<.001) greater mean fitness score than non-athletes (Mean=39.8, SD=4.8). Conclusion: This study presents a valid equation that can simply predict overall health-related fitness in college students.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 224-231. DOI: 10.12691/ajams-6-6-2
Pub. Date: November 07, 2018
11062 Views1663 Downloads
by Ben K. Koech
Original Research
Receiver operating characteristic curve analysis is widely used in biomedical research to assess the performance of diagnostic tests. Estimation of receiver operating characteristic curves based on parametric approach has been widely used over years. However, this is limited by the fact that distribution of almost all diseases in epidemiology cannot be established quite easily. Semi parametric methods are robust as it allows computability and the distributions based on this are flexible. Furthermore, there is need for generalization of the receiver operating characteristic curve (since, the analysis largely assumes that test results are dichotomous) to allow tests to have more than two outcomes. The receiver operating characteristic curve was generalized to constitute a surface, which uses volume under the surface (VUS) to measure the accuracy of a diagnostic test. Dirichlet process mixtures of normals, which is a robust model that can handle nonstandard features in data in modelling the diagnostic data, were used to model the test outcomes. Semiparametric Dirichlet process mixtures of normals for receiver operating characteristic surface estimation were fitted using Markov Chain Monte Carlo with simple Metropolis Hastings steps. The Semi-parametric simulation results indicate that even when the parametric assumption holds, these models give accurate results as the volume under the surface (VUS) for both methods were greater than 1/6, the value of a “useless test”. Graphically, the semiparametric receiver operating characteristic surface has the appealing feature of being continuous and smooth, thus allowing for useful interpretation of the diagnostic performance at all thresholds.
American Journal of Applied Mathematics and Statistics. 2018, 6(6), 218-223. DOI: 10.12691/ajams-6-6-1
Pub. Date: October 31, 2018
10003 Views2162 Downloads2 Likes