Open Access Original Research Article

Optimization of Split-Plot Design in the Context of Mixture Process Variable Settings

Samson W. Wanyonyi, Ayubu A. Okango, Julius K. Koech, Betty C. Korir

Asian Journal of Probability and Statistics, Page 1-36
DOI: 10.9734/ajpas/2021/v12i330285

In the presence of process variables, a mixture design has become well-known in statistical modeling due to its utility in modeling the blending surface, which empirically predicts any mixture's response and serves as the foundation for optimizing the expected response blends of different components.  In the most common practical situation involving a mixture-process variable, restricted randomization occurs frequently. This problem is solved when the split-plot layout arrangement is used within the constraints. This study's primary goal was to find the best split-plot design (SPD) for the settings mixture-process variables. The SPD was made up of a simplex centroid design (SCD) of four mixture blends and a factorial design with a central composite design (CCD) of the process variable and compared six different context split-plot structure arrangement.  We used JMP software version 15 to create D-optimal split-plot designs. The study compared the constructed designs' relative efficiency using A-, D-, I-, and G- optimality criteria. Furthermore, a graphical technique (fraction of design space plot) was used to display, explain, and evaluate experimental designs' performance in terms of precision of the six designs' variance prediction properties. We discovered that arranging subplots with more SCD points than pure mixture design points within SPD with two high process variables is more helpful and provides more precise parameter estimates. We recommend using SPDs in experiments involving mixture process settings developments to measure the mixture components' interaction effects and the processing conditions. Also, the investigation should be set up at each of the points of a factorial design.

Open Access Original Research Article

Modeling of Seasonal Multivariate Time Series Analysis; Using Gross Domestic Product (GDP) in Nigeria (January 1985- 2017)

Ekpenyong Aniedi Moses, Ette Harrison Etuk

Asian Journal of Probability and Statistics, Page 46-58
DOI: 10.9734/ajpas/2021/v12i330288

The multivariate “Seasonal Vector Autoregressive Moving Average” was used to measure the growth rate of Gross Domestic Product (GDP) in five (5) sectors: Agriculture, Industries, Building/Construction, Wholesales/Retails, and Services. The data was gathered from the National Bureau of Statistics and spans 33 years, from 1985 to 2017. To evaluate the model, real (R) software was used. The variability statistics for the five variables show that all of the variables have a seasonality pattern that is not stationary. We difference the data series (once) to obtain stationary series and define the season order to indicate the seasonality pattern. We find the best model using Akaike information criteria and Bayesian information criteria. The best model was determined to be the SVARMA (4, 1, 1) (1, 0, 0)12. We also apply model simplification to the SVARMA (4, 1, 1) (1, 0, 0), 12 model, to exclude statistically insignificant parameters. The forecasts revealed that the rate of growth in the Agriculture sector is slowly growing, the rate of growth in the Industries sector is slowly decreasing, the rate of growth in the Building/Construction sector is increasing, the rate of growth in the Wholesales/Retails sector is not stable, and the rate of growth in the services sector is poor.

Open Access Original Research Article

ARIMA Modelling and Forecasting of COVID-19 Daily Confirmed/Death Cases: A Case Study of Nigeria

Essi Isaac Didi, Nwuju Kingdom, Etuk Ette Harrison

Asian Journal of Probability and Statistics, Page 59-80
DOI: 10.9734/ajpas/2021/v12i330289

Aims: The aim of this work is to develop suitable ARIMA models which can be sued to forecast daily confirmed/death cases of COVID-19 in Nigeria. This is subject to developing the model, checking them for suitability and carrying out eight months forecast, and making recommendations for the Nigerian Health sector.

Study Design:  The study used daily confirmed and death cases of COVID-19 in Nigeria.

Methodology: This work covers times series data on the on the daily confirmed/death cases of COVID-19 in Nigeria, obtained from the Nigerian Centre for Disease Control (NDCD) from 21 March 2020 to 5 May 2020, covering a total of 51 data points. This work  is geared towards developing a suitable  Autoregressive Integrated Moving Average (ARIMA) models which can be used to forecast total daily confirmed/death cases of COVID-19 in Nigeria. Two adequate subset ARIMA (2, 2, 1) and AR (1) models for the confirmed/death cases, respectively, is fitted and discussed

Results: A forecast of 239 days – from 6th May 2020 to 31 December 2020 was conducted using the fitted models and we observed that the COVID19 data has an upward trend and is best forecasted within a short period.

Conclusion: Critical investigation into the rate of spread of COVID-19 pandemic has shown that, that the daily confirmed cases as well as death cases of the disease tends to follow an upward trend. This work aimed at developing a suitable ARIMA models which can be used to fit a most appropriate subsets  to statistically forecast the actual number of confirmed cases as well as death cases of COVID-19 recorded in Nigeria for a period of 8 months.

Open Access Review Article

Sarima Modeling of Monthly Temperature in the Northern part of Ghana

Emmanuel Ayitey, Justice Kangah, Frank B. K. Twenefour

Asian Journal of Probability and Statistics, Page 37-45
DOI: 10.9734/ajpas/2021/v12i330287

The Sarima model is used in this study to forecast the monthly temperature in Ghana's northern region. The researchers used temperature data from January 1990 to December 2020. The temperature data was found to be stationary using the Augmented Dickey Fuller (ADF) test. The ACF and PACF plots proposed six SARIMA models: SARIMA (1,0,0) (1,0,0) (12), SARIMA (2,0,0) (1,0,0) (12), SARIMA (1,0,1) (1,0,0) (12), SARIMA (0,0,1) (1,0,0) (12), SARIMA (0,0,1) (0,0,1) (12), SARIMA (0,0,1) (0,0,1) (12). The best model was chosen based on the lowest Akaike Information Criteria (AICs) and Bayesian Information Criteria (BIC) values. The Ljung-Box data, among others, were used to determine the model's quality. All diagnostic tests are passed by the SARIMA (1,0,0) (1,0,0) (12) model. As a result, the SARIMA (1,0,0) (1,0,0) (12) is the best-fitting model for predicting monthly temperatures in Ghana's northern region.

Open Access Review Article

Review of Different Types of Energy and Some Properties of Semiregular Graphs

J. Visuvasam, S. Thamizh Suganya

Asian Journal of Probability and Statistics, Page 81-101
DOI: 10.9734/ajpas/2021/v12i330290

In this paper, some properties of semi-regular graphs have been studied. The energy of graphs has many mathematical properties, which are being investigated for some of the semi-regular graphs. Also, the Laplacian Energy of these types of the graph has been defined has also been studied. We give examples of semi-regular graphs, describe the barbell class, and describe how the property of semi regularity relates to other properties of graphs.