by K.M. Sakthivel and C.S. Rajitha
Original Research
Zero inflated models have been widely studied in statistical literature. Zero inflated Poisson model and hurdle model are the most commonly used models for modeling the overdispersed count data. In adddition to this, recent studies shows that a nonparametric and data dependent technique known as artificial neural networks (ANN) produce better performance for modeling the over dispersed and zero inflated count data. In this paper, we compared the performance of different models such as zero inflated Poisson model, hurdle model and ANN for modelling the zero inflated count data in terms of standardized MSE, SE, bias and relative efficiency. An application study is carried out for both the simulated data set and real data set. Also for checking the suitability of these three models, we verified the group membership of the models, by adopting three classification techniques known as discriminant analysis, CART and random forest. We proposed an algorithm for selecting the better model among a set of models and computed the misclassification rates for a zero inflated count data set using different classifiers.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 43-51. DOI: 10.12691/ajams-7-1-7
Pub. Date: January 15, 2019
18305 Views2304 Downloads
by Dina H. Abdel Hady
Original Research
This paper deals with random removal of progressively type II censored data. The removal of the data is assumed to follow a binomial or a uniform distribution, and the life time testing is assumed to follow a Gompertz distribution. Parameters of these distributions are estimated using the Maximum Likelihood estimation procedure. Fisher information matrix is used to estimate the asymptotic mean squared error and to construct confidence intervals of model parameters. The optimal partially accelerated lifetime testing (PALT) is estimated by minimizing the Generalized Asymptotic Variance (GAV). Simulation study is performed to Clarification the statistical properties of the parameters. A simulation results reveal that for the fixed values of the parameters, the error and optimal time decrease with increasing sample size n; estimates of binomial are more stable with a relatively small error with increasing sample size; and the test design is robust and works well for binomial removal.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 37-42. DOI: 10.12691/ajams-7-1-6
Pub. Date: January 01, 2019
7300 Views1989 Downloads
by George Nchelem Rosemary and Charles-Ogan Gladys Ibibo
Original Research
Aptitude tests are used globally for academic admission and job placement. This study, therefore, employed the correlational research design to investigate the relationship between students’ Mathematics achievement and quantitative reasoning ability in junior secondary schools in Rivers State Nigeria. Three objectives, three research questions and three null hypotheses were tested at 0.05 alpha level. The population was 1, 853 junior secondary school three (JSS3) students in the public co-educational junior secondary schools in Asari-Toru Local Government Area of Rivers State, Nigeria. A 2-stage simple random sampling technique was used to select a sample of sixty-one students. Two validated and reliable instruments titled Mathematics Cognitive Achievement Test (MCAT; r =0.81) and Quantitative Reasoning Ability Test (QRAT; r =0.73) were used to collect data. All the sample students were taught some selected Mathematics topics and how to observe, identify patterns and apply basic mathematical skills to resolve quantitative reasoning test items. Mean, standard deviation and Pearson Product Correlation was used for analysis. The result showed that there is a moderate positive relationship between students’ Mathematics achievement and their quantitative reasoning ability. Gender wise, the result revealed that there is a moderate positive relationship between the female students’ Mathematics achievement and their quantitative reasoning ability while there is a positive fair relationship between the male students’ Mathematics achievement and their quantitative reasoning ability. It was therefore recommended amongst others that quantitative reasoning should be learnt in schools as a subject on its own to allow more time for grooming of its skills and processes.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 32-36. DOI: 10.12691/ajams-7-1-5
Pub. Date: January 01, 2019
8199 Views2096 Downloads
by WMND Basnayake, MDT Attygalle, Liwan Liyanage-Hansen and KDW Nandalal
Original Research
In spite of the ability of Artificial Neural Network (ANN) to handle nonlinear relationships in data, there are instances where ANNs have not been able to predict accurately in the presence of non-stationarity. A novel algorithm that has the ability to treat the nonstationary and nonlinearity in a time series had been presented in [1]. This paper presents a modification done to the algorithm via addressing the edge distortion that arises in the real time execution. The proposed algorithm in [1] was named as “1D Multilevel DWT Segmented ANN Algorithm” where the modified algorithm presented in this paper will be called as “Denoised 1D Multilevel DWT Segmented ANN Algorithm”.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 25-31. DOI: 10.12691/ajams-7-1-4
Pub. Date: January 01, 2019
8805 Views859 Downloads
by P. K. Sahu, Soumik Dey, Kanchan Sinha, Herojit Singh and L. Narsimaiaha
Original Research
Price discovery is one of the major functions of the commodity market to hedge sharp price fluctuations, protecting the interests of both farmers and consumers. Production and export of major spices from India is gradually gaining importance in foreign market and also on Indian economy in terms of foreign currency reserve. This study makes an effort to understand the price discovery mechanism byidentifying the transmission of price signals between spot and futures market of four major spices (chilli, turmeric, cumin and coriander) that are traded in National Commodity and Derivative Exchange (NCDEX), India using daily price data from October 2015 to April 2017. Among other statistical tools, econometric methods viz., Cointegration test, Granger Causality test, Vector Error Correction Model (VECM) are used in assessing the price behavioural pattern between spot and futures market. Cointegration analysis reveals long run associationship between spot and futures prices in chilli,turmeric, cumin. The study also reveals that both spot and futures market play leading role in the price discovery process and are informationally efficient in reacting to each other. On the other hand uni-directional causality is evident from futures to spot price in case of coriander. It is expected that both the producers and the users of these important spices will be benfitted from such findings and will help them in harvesting better profit by hedging out the uncertainity in the spice market.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 18-24. DOI: 10.12691/ajams-7-1-3
Pub. Date: December 28, 2018
8893 Views1299 Downloads
by K.A.D. Deshani, Liwan Liyanage-Hansen and Dilhari Attygalle
Original Research
This paper presents the procedure of building a dynamic predictive model using an artificial neural network to perform an iterative forecast. An algorithm is proposed and named as “Artificial Neural Network Approach for Dynamic Iterative Forecasting”. The development of this algorithm focused on feature selection, identification of best network architecture for the model, moving window selection and finally the iterative prediction. This proposed algorithm was deployed to forecast next day’s hourly total demand in Sri Lanka as an illustration. Inclusion of a clustering effect that were based on the specialty of the day, as an input was investigated through this application, from which improved accuracies were shown.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 9-17. DOI: 10.12691/ajams-7-1-2
Pub. Date: December 25, 2018
12672 Views1948 Downloads
by Nneamaka Judith Ezeagu, Houénafa Alain Togbenon and Edwin Moyo
Original Research
A mathematical model for the transmission of cholera dynamics with a class of quarantined and vaccination parameter as control strategies is proposed in this paper. It is shown through mathematical analysis that the solution of the model uniquely exist, is positive and bounded in a certain region. The disease-free and endemic equilibrium points of the model are obtained. By using the next generation matrix, the basic reproduction number was computed around the disease-free equilibrium points, and it was shown through the Jacobian matrix that the disease free equilibrium is locally asymptotic stable if Rh<1. Numerical simulation was carried to understand the impact of the incorporated controls as the system evolves over time. Results show that effective quarantine, vaccination and proper sanitation reduce the disease contact rates and thus eliminates the spread of cholera.
American Journal of Applied Mathematics and Statistics. 2019, 7(1), 1-8. DOI: 10.12691/ajams-7-1-1
Pub. Date: December 24, 2018
10562 Views2347 Downloads