Open Access Original Research Article

Efficiency and Consistency Assessment of Value at Risk Methods for Selected Banks Data

Yakubu Musa, Iniabasi Emmanuel Etuk, S. U. Gulumbe

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/jamcs/2020/v35i230245

The study assesses Value at Risk (VaR) methods with respect to their efficiency and consistency in selected banks of the Nigeria Stock Market. The daily data on share prices of each bank was used from 2006 to 2018. The Value at Risk of each bank was estimated and the predictive performance of each method was assessed using the Failure Ratio and the Confidence Interval. The quality of each method was assessed based on the efficiency and consistency of the estimates. The VaR of each bank was estimated using Historical Simulation, Kernel Estimator, Empirical Estimator and Weighted Mean methods. The weighted mean method had the least estimates while Kernel estimator method had the highest estimates. The Failure Ratio and Confidence Interval show that Historical and Empirical methods had the least number of rejections at both confidence levels. The efficiency and consistency of the various methods shows the Historical Simulation and Weighted mean method had the minimum mean square errors (MSE). The Banks A, D and E gives an efficient and consistent result with Historical Simulation while B and C, is more efficient and consistent with weighted mean method.

Open Access Original Research Article

Relative Extension of Continuous Mappings

Miroslaw Slosarski

Journal of Advances in Mathematics and Computer Science, Page 12-24
DOI: 10.9734/jamcs/2020/v35i230246

In this paper, the notion of a relative extension of continuous mappings is defined. The relative extension of continuous mappings is the generalization of the notion of a relative retract in topological spaces. The relative extension of continuous mappings will be applied to fixed point theory.

Open Access Original Research Article

Security Detection in Audio Events: A Comparison of Classification Methods

Alissar Nasser

Journal of Advances in Mathematics and Computer Science, Page 25-41
DOI: 10.9734/jamcs/2020/v35i230247

The security of public places is becoming important with the increased rate of violence and subversion. Recently, several types of research have been proposed to automatically detect abnormal behavior in public places like a car crash, violence or other hazardous events in an attempt to improve security and save lives. Furthermore, most of the researches are using supervised classifications techniques to classify the audio signals. This paper proposes the use of the kernel principal component analysis (KPCA) to reduce the number of MFCC features extracted from the audio signal and then apply an unsupervised classification algorithm. Moreover, this paper presents the results of several supervised and unsupervised classification methods for audio events detection and compares these results with the result of the proposed approach. Experiments are done using a real data set recorded at the mean of public transportation. The obtained results reveal that K-means on 2 KPCA components gave good results for triggering a true alarm as well as detecting a false alarm; where the percentages of false and missed alarms were 4.5% and 7.8% respectively; whereas these values were 0.8% and 9.3% respectively for kernel k-means. Notwithstanding the DNN network gave the best results with a false alarm rate of 0% and 1.4% missed alarm.

Open Access Original Research Article

On Generalized Grahaml Numbers

Yuksel Soykan

Journal of Advances in Mathematics and Computer Science, Page 42-57
DOI: 10.9734/jamcs/2020/v35i230248

In this paper, we introduce the generalized Grahaml sequences and we deal with, in detail, three special cases which we call them Grahaml, Grahaml-Lucas and modified Grahaml sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Open Access Original Research Article

Application of a Novel Fractional Order Grey Support Vector Regression Model to Forecast Wind Energy Consumption in China

Jiahao Cao, Liang Liu, Lizhi Yang, Shuchuan Xie

Journal of Advances in Mathematics and Computer Science, Page 58-69
DOI: 10.9734/jamcs/2020/v35i230249

In order to achieve accurate prediction of new energy related data, a fractional grey support vector regression model based on nested cross-validation is proposed. In order to verify the superiority of the new model, China’s wind energy consumption data from 2001 to 2014 were selected, and a fractional grey prediction model, a support vector regression model and a fractional support vector regression combination model were established, and wind energy consumption in China was predicted from 2015 to 2018. Numerical experimental results show that the newly proposed combined prediction model has higher prediction accuracy.

Open Access Original Research Article

Application of a New Information Priority Accumulated Grey Model with Simpson to Forecast Carbon Dioxide Emission

Xiwang Xiang, Yubin Cai, Shuchuan Xie

Journal of Advances in Mathematics and Computer Science, Page 70-83
DOI: 10.9734/jamcs/2020/v35i230250

Climate warming is a hot topic of common concern all over the world and it has had a significant impact on climate, oceans and human life. The increase in the concentration of carbon dioxide in the atmosphere has become a significant factor in climate warming. In recent years, the concentration of carbon dioxide in the atmosphere has been mostly anthropogenic emissions. Accurate forecasting of carbon dioxide emissions will effectively propose solutions to the problem of global warming and then improve the environment in which we live. In our work, first of all, we use the new information priority accumulation method to optimize the weight of the new information in the prediction. Then we use the numerical integration method to optimize the background value of the grey model to achieve more accurate forecast. Application case results show that our proposed model is superior to other grey models in predicting carbon dioxide emission in India and Bangladesh.

Open Access Original Research Article

A Novel Modification of Adomian Decomposition Method for Singular BVPs of Emden-Fowler Type

Somaia Ali Alaqel, Yahya Qaid Hasan

Journal of Advances in Mathematics and Computer Science, Page 84-100
DOI: 10.9734/jamcs/2020/v35i230251

In this paper, we apply a novel Modied of Adomian Decomposition Method (MADM) for solving Singular Boundary Value Problems (BVPs) of Emden-Fowler type of higher order. The higher-order Emden-Fowler equation is characterized by two types. In addition, we test the presented method by several linear and nonlinear examples, and compared the numerical result with the exact solution to illustrate performance and reliability of this method in nding approximate solutions as well as its successful in getting the complete solution in many case.

Open Access Original Research Article

Modelling of COVID-19 Transmission in Kenya Using Compound Poisson Regression Model

Joab O. Odhiambo, Philip Ngare, Patrick Weke, Romanus Odhiambo Otieno

Journal of Advances in Mathematics and Computer Science, Page 101-111
DOI: 10.9734/jamcs/2020/v35i230252

Since the inception of the novel Corona Virus Disease-19 in December in China, the spread has been massive leading World Health Organization to declare it a world pandemic. While epicenter of COVID-19 was Wuhan city in China mainland, Italy has been affected most due to the high number of recorded deaths as at 21st April, 2020 at the same time USA recording the highest number of virus reported cases. In addition, the spread has been experienced in many developing African countries including Kenya. The Kenyan government need to make necessary plans for those who have tested positive through self-quarantine beds at Mbagathi Hospital as a way of containing the spread of the virus. In addition, lack of a proper mathematical model that can be used to model and predict the spread of COVID-19 for adequate response security has been one of the main concerns for the government. Many mathematical models have been proposed for proper modeling and forecasting, but this paper will focus on using a generalized linear regression that can detect linear relationship between the risk factors. The paper intents to model and forecast the confirmed COVID-19 cases in Kenya as a Compound Poisson regression process where the parameter follows a generalized linear regression that is influenced by the number of daily contact persons and daily flights with the already confirmed cases of the virus. Ultimately, this paper would assist the government in proper resource allocation to deal with pandemic in terms of available of bed capacities, public awareness campaigns and virus testing kits not only in the virus hotbed within Nairobi capital city but also in the other 47 Kenyan counties.

Open Access Original Research Article

On a Retrial Queueing Model with Customer Induced Interruption

Varghese Jacob

Journal of Advances in Mathematics and Computer Science, Page 112-120
DOI: 10.9734/jamcs/2020/v35i230253

This paper presents a retrial queueing system with customer induced interruption while in service. We consider a single server queueing system of infinite capacity to which customers arrive according to a Poisson process and the service time follows an exponential distribution.
An arriving customer to an idle server obtains service immediately and customers who find server busy go directly to the orbit from where he retry for service. The inter-retrial time follows exponential distribution. The customer interruption while in service occurs according to a Poisson process and the interruption duration follows an exponential distribution. The customer whose service is got interrupted will enter into a finite buffer. Any interrupted customer, finding the buffer full, is considered lost. Those interrupted customers who complete their interruptions will be placed into another buffer of same size. The interrupted customers waiting for service are given non-preemptive priority over new customers. We analyse the steady-state behavior of this queuing system. Several performance measures are obtained. Numerical illustrations of the system behaviour are also provided with example.

Open Access Review Article

Recommender Systems: Algorithms, Evaluation and Limitations

Mubaraka Sani Ibrahim, Charles Isah Saidu

Journal of Advances in Mathematics and Computer Science, Page 121-137
DOI: 10.9734/jamcs/2020/v35i230254

Aims/ objectives: This paper presents the different types of recommender filtering techniques. The main objective of the study is to provide a review of classical methods used in recommender systems such as collaborative filtering, content-based filtering and hybrid filtering, highlighting the main advantages and limitations. This paper also discusses the state-of-art machine learning based recommendation models including Clustering models and Bayesian Classifiers. Further, we discuss the widespread application of recommender systems to a variety of areas such as e-learning and e-news. Finally, the paper evaluates the performance of matrix factorization-based models, nearest neighbours algorithms and co-clustering algorithms in terms of different metrics.