Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 6Akintunde Mutairu O., Chigozie Kelechi A., Agunloye Oluokun K., Oyekunle Janet O., Agbona Anthony A., Kgosi Phazamile M.The paper provides an understanding about the theoretical and empirical illustration of working of various classes of ARCH family models used in the study. It equally exploits the potential benefits derivable from using this family type models. It dwells heavily into the best time series model among autoregressive moving average (ARMA), Autoregressive conditional heteroscedasticity (ARCH), Generalized Autoregressive conditional heteroscedasticity (GARCH), Integrated Generalized Autoregressive conditional heteroscedasticity (IGARCH), Threshold Generalized Autoregressive conditional heteroscedasticity (TGARCH) and Exponential Generalized Autoregressive conditional heteroscedasticity (EGARCH) models, and determined the models which actually give the best forecast performance. Mathematical background of all these models were set up and promptly illustrated using monthly data of number of patients admitted for malaria at Ladoke Akintola teaching hospital, Osogbo. It covers the period of five years (2012 January to December, 2016), obtained from the hospital record of LAUTECH, Osogbo. Stationarity tests (graph, unit root and correlgram) were conducted before proceeding to parameter estimations. The grid search using Akaike information criteria (AIC) and Performance measures indices were used to determine the best model. So also, performance measure indices were cross tabulated with the models. In all, out of seven performance measure indices used, EGARCH (1,1) Model is best in the six of the indices. From these results EGARCH (1,1) is recommended for would be investors, forecasters and other categories of users.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 6Fatoki OlayodeWe introduce a new lifetime distribution which is the generalization of Rayleigh distribution using the Topp-Leone generated family of distributions proposed by Rezaei et al. The new distribution is called the Topp-leone Rayleigh (TLR) distribution. The new distribution was found to be more flexible in modeling data that exhibits increasing, decreasing, non-monotone failure rate. Expressions for several probabilistic measures were provided, such as probability density function, hazard function, moments, quantile function, mean, variance and median, moment generating function, orders statistics etc. Inference is maximum likelihood based and tractability of model was shown by its application to a real data set.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 6Nduka Wonu, Reginald Ugochukwu OrluThis study modelled time-series data on the Mathematics achievement of senior secondary students for a period of twenty-nine (29) years. Trend analysis and Autoregressive Integrated Moving Average (ARIMA) techniques were employed in this study to determine the trend and forecast values that fitted the series (“linear and quadratic” trend). The result of the analysis revealed that the line graph was not stationary because of the change invariance. Unit Root Stationary Test conducted using the Augmented Dicky-Fuller Test (ADF) later confirms the line graph of the achievement of secondary school students in Mathematics, not stationarity because the p-value of 0.124 is greater than 0.05. The time plot of the first difference became stationary. The stationarity condition of the data series are observed by ACF and PACF plots and then checked using the statistic such as ADF. The model for which the values of the criteria are smallest is considered as the best model. ARIMA (2,1,0) is the best fit model based on the Akaike Information Criterion (AIC). Hence the residual analysis for ARIMA (2,1,0) fitted to the achievement of secondary school students in Mathematics data fits quite well.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 5Ajay Kumar Chaudhary, Kanhaiya JhaThe classical Banach contraction principle in metric space is one of the fundamental results in metric space with wide applications. And the probabilistic metric space is one of the important generalizations of metric space introduced by Austrian mathematician Karl Menger in 1942. The purpose of this article is to describe different contraction conditions in Probabilistic Metric Space. Also, mention the generalized contraction conditions and interrelationships between contraction conditions.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 5Emmanuel Kojo AmoahThe current changes in ecosystem functioning and climate systems are having major impact on Fire Outbreaks conditions globally. It is worrying that not much work appears to have been done in Ghana regarding the formulation of statistical and other models for predicting Fire Outbreaks. Due to this, actuarial and insurance practitioners are unable to effectively help manage the risk of Fire Outbreaks. This study sought to predict monthly fire outbreaks by employing the Box-Jenkins approach to model fire outbreaks using time series data from 1997 to 2014. Several SARIMA (Seasonal Auto Regressive Integrated Moving Average) models were tested and the model with lowest Akaike Information Criterion (AIC) was selected. The analysis revealed that ARIMA (4, 1, 1) (1, 1, 1)12 model was the best SARIMA model for the Fire Outbreaks since diagnostic checks revealed its adequate for predicting the monthly number of fire outbreaks in Ashanti Region of Ghana. The sixteen years forecast with this model revealed that the number of fire outbreaks will continue to increase with time. This continuous increase in the pattern of the number of fire outbreaks as evident from the forecast results could be a great danger to the economy of the country. The results achieved for fire forecasting will help to estimate number of fire events which can be used in planning the fire activities in that region. The study recommends that, stakeholders and management of fire should make use of this formulated SARIMA model for the purpose predicting, mitigating and insuring against fire outbreaks in Ghana.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 5Md. Shahajada Mia, Md. Siddikur RahmanExchange rate is the price of one currency in terms of another currency. Modelling exchange rate volatility can play an important role in macroeconomic management for stability and growth. This paper examine the forecasting accuracy of ARCH family models for the monthly BDT/ USD exchange rate data from Bangladesh Bank over the period from August, 2004 to April, 2019. To find an appropriate model, several model selection criterion: Akaike information criteria (AIC) and Schwarz information criteria (SIC) and for measuring accuracy Root mean squared error (RMSE), Mean absolute error (MAE), Mean absolute percentage error (MAPE) and Theil inequality (TI) are used. Evaluation of models through these criteria suggest that GARCH (1,1) model is the best model for forecasting the monthly exchange rate volatility of Bangladesh and successfully overcome the leverage effect in the exchange rate.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 4Nwakuya M. T., Biu E. O.This study examines the within-group and first difference fixed effect models using panel data set. Panel data on GDP, inflation, trade, civil-liability and population were collected across six African countries between 1972 and 1991, the data is an inbuilt R data found in amelia package. Performance of these fixed effect models were compared in terms of fitness using R- squared and relative efficiency. Results were generated using R software. Finding shows that in the within-group model, trade was the only independent variable that contributes significantly to GDP but in the first difference model both trade and population contributed significantly to GDP. The finding also reveals that within group model had a better fit with an R2 of 0.77317 as compared to first difference model which reported R2 of 0.75472. The relative efficiency was determined to be 1.3 showing that relative to within-group model the first difference model is preferred.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 4Benjamin Boniface, Abiodun O. AjibadeNatural convection double diffusive flow heat generating fluid in a vertical channel has been examined. Diffusion-thermo (Dufour) and heat generating effects are also considered. Suitable transformations are employed to convert the partial differential equations representing the concentration, temperature and velocity into a system of ordinary differential equations. Approximate solutions are obtained for velocity, skin-friction, temperature, heat transfer, concentration and mass transfer by the use of a two-term harmonic and non-harmonic perturbation method. The result for the mixture of carbon dioxide in air are presented graphically. It is found that the velocity decreases with increasing slip while it increases with increasing thermal diffusion Also the mean skin-friction M and the phase of the rate of heat transfer N increases with increase in the buoyancy parameter as well as Dufour effect while both the temperature and concentration increase near the hot plate and decreases exponentially towards the cold plate.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 4S. Shams, H. Rashidi, S. RezaeeRecently by using contamination families, a new way of modeling dependence has been introduced. In this method, a sequence of parametric copulas is considered and in a few numbers of steps, accurate approximations for copula densities are obtained. By using the selection model method, the model complexity and number of model parameters are balanced. In this paper, two main variables in Iranian Household Income and Expenditure survey are considered and a copula density for those variables is estimated by using contamination family and selection model method.

Abstract: Publication year: 2019Source: American Journal of Mathematics and Statistics, Volume 9, Number 4Kofi Agyarko, Albert Buabeng, Joseph AcquahThis study assessed the volatility and the Value at Risk (VaR) of daily returns of Bitcoins by conducting a comparative study in the forecast performance of symmetric and asymmetric GARCH models based on three different error distributions. The models employed are the SGARCH and TGARCH which were validated based on AIC, MAE and MSE measures. The results indicated that the SGARCHGED (1,1) with generalised error distribution term was identified as the best fitted GARCH model. Though, this best fitted model based on information loss (AIC) did not provide the best out-of-sample forecast, the differences was insignificant. Thus, the study clearly demonstrates that it is reliable to use the best fitted model for volatility forecasting. Also, to further validate the performance of the best fitted model, it was subjected to a historical back-test using Value at Risk (VaR). Though, it was evident from the study that no model was superior, it was indicated that an average loss of 1.2% is expected to be exceeded only 1% of the time. Moreover, volatility forecast from the back testing was relatively high during the first quarter of 2018 but begun decreasing steadily with time.