##### Optimal Prediction Variance Capabilities of Inscribed Central Composite Designs

Julius C. Nwanya, Kelechukwu C. N. Dozie

Asian Journal of Probability and Statistics, Page 1-8
DOI: 10.9734/ajpas/2020/v8i130194

This study looks at the effects of replication on prediction variance performances of inscribe central composite design especially those without replication on the factorial and axial portion (ICCD1), inscribe central composite design with replicated axial portion (ICCD2) and inscribe central composite design whose factorial portion is replicated (ICCD3). The G-optimal, I-optimal and FDS plots were used to examine these designs. Inscribe central composite design without replicated factorial and axial portion (ICCD1) has a better maximum scaled prediction variance (SPV) at factors k = 2 to 4 while inscribe central composite design with replicated factorial portion (ICCD3) has a better maximum and average SPV at 5 and 6 factor levels. The fraction of design space (FDS) plots show that the inscribe central composite design is superior to ICCD3 and inscribe central composite design with replicated axial portion (ICCD2) from 0.0 to 0.5 of the design space while inscribe central composite design with replicated factorial portion (ICCD3) is superior to ICCD1 and ICCD2 from 0.6 to 1.0 of the design space for factors k = 2 to 4.

##### An Effcient Method to Find Approximate Solutions for Emden-Fowler Equations of nth Order

Nuha Mohammed Dabwan, Yahya Qaid Hasan

Asian Journal of Probability and Statistics, Page 9-27
DOI: 10.9734/ajpas/2020/v8i130195

In this research, Emden-Fowler equations of higher order with boundary conditions are considered and solved using Modied Adomian Decomposition Method (MADM). We dened a new differential operator under two conditions: rst condition when m ≤ 0 and second condition when m ≥ 0. From this operator, we got three types of Emden-Fowler equations of higher order. The new method is evaluated by using many examples, the results obtained through this method reveal the effectiveness of this method for these type of equations, especially when comparisons are made with the exact solution.

##### The Hamza Distribution with Statistical Properties and Applications

Ahmad Aijaz, Muzamil Jallal, S. Qurat Ul Ain, Rajnee Tripathi

Asian Journal of Probability and Statistics, Page 28-42
DOI: 10.9734/ajpas/2020/v8i130198

This paper suggested a new two parameter distribution named as Hamza distribution. A detailed description about the properties of a suggested distribution including moments, moment generating function, deviations about mean and median, stochastic orderings, Bonferroni and Lorenz curves, Renyi entropy, order statistics, hazard rate function and mean residual function has been discussed. The behavior of a probability density function (p.d.f) and cumulative distribution function (c.d.f) have been depicted through graphs. The parameters of the distribution are estimated by the known method of maximum likelihood estimation. The performance of the established distribution have been illustrated through applications, by which we conclude that the established distribution provide better fit.

##### A Note on Second Order Slope Rotatable Designs under Intra-class Correlated Errors Using Pairwise Balanced Designs

K. Rajyalakshmi, B. Sulochana, B. Re. Victorbabu

Asian Journal of Probability and Statistics, Page 43-54
DOI: 10.9734/ajpas/2020/v8i130199

In this paper, a study on second order slope rotatable designs under intra-class correlation structure of errors using pairwise balanced designs is suggested. Further, the variance function of the estimated slopes for different values of intra-class correlated coefficient ‘ ’ for 6 ≤ v ≤ 15 (v- number of factors) are studied.

##### Modeling and Forecasting Exchange Rate Values between Naira and US Dollar to Assess the Effect of COVID-19 Pandemic Period on the Rate

E. J. Okon, I. N. Ikpang

Asian Journal of Probability and Statistics, Page 55-65
DOI: 10.9734/ajpas/2020/v8i130200

Aims: To model exchange rate values between Naira and US Dollar in order to assess the effect of the COVID-19 pandemic period on the rate by examining the forecasts.

Study Design: The study design is the longitudinal research design.

Place and Duration of Study: Real life data of monthly average Nigerian Naira-US Dollar exchange rates from Jan.1991 to April 2020 obtained from the Data and Statistics publication of Central Bank of Nigeria.

Methodology: The traditional time series ARIMA model is employed for forecasting Naira/Dollar exchange rate using Monthly data covering the period January, 1991 to April, 2020. The ACF and PACF plots showed tendency that the differenced exchange rate data behave as both having autoregressive and moving average processes as the ACF has significant peaks at different lags and a gradual decay to zero is indicated by the PACF.

Results: Using the AIC, BIC, and HQC as model selection criterion the ARIMA (2, 1, 3) were selected as the model with the best fit for the exchange rate data as compared to the other selected models. The ACF of the residuals is plotted with lags up to 20 and the residuals coefficient did not exceed the 95% confidence limit which indicates that the model is a good fit and is appropriate for the data. Plots of in-sample and out-of-sample forecast were also made.

Conclusion: The out-of-sample forecast plot for period of 12 months revealed that naira will continue to depreciate on US dollar for the period forecasted with very high tendencies during the COVID-19 pandemic period.