Open Access Original Research Article

Comparison of Metamodel Performances on an Electronic Circuit Problem

Muzaffer Balaban

Asian Journal of Probability and Statistics, Page 1-11
DOI: 10.9734/ajpas/2021/v11i230261

Aims: Investigation of building and validation of metamodels which of linear regression, simple kriging, ordinary kriging and radial basis function for an electronic circuit problem are the main aim of this study.

Study Design: An electronic circuit problem was considered to compare the performances of the metamodels. Latin hypercube design was used for experimental design of five input variables of the considered problem.

Methodology: A training data set consisting of 45 experiments and a validation data set consisting of 500 experiments were obtained using Latin hypercube design. Input variables were used by coded to calculate the spatial distances between observation points more consistently. Then using training data set linear regression, simple kriging, ordinary kriging and radial basis function metamodels were built. And, performance measures were calculated for the validation data set.

Results: It has been shown that simple kriging which are applied to outputs the differences from the mean, and ordinary kriging metamodels, produce superior solutions compared to the linear regression and radial basis function metamodels for the electronic circuit problem considered in this study. Prediction superiority of SK and OK than RBF on five-dimensional problem is another important result of the study.

Conclusion: Kriging metamodels are considered to be strong alternatives to the other metamodels for the problems that are considered in this study and have a similar nature. Since the superiority of metamodel methods to each other may vary from problem to problem, it is another important issue to compare their performance by considering more than one method in problem solving stage.

Open Access Original Research Article

The Theoretical Overview of Generalized Gumbel Type-Ⅱ Distribution

S. Qurat Ul Ain, Ahmad Aijaz, Rajnee Tripathi

Asian Journal of Probability and Statistics, Page 21-29
DOI: 10.9734/ajpas/2021/v11i230263

A new version of weighted model is introduced by assigning weights to Gumbel Distribution Type Ⅱ (GDT-Ⅱ) to make it more useful and flexible in life time data .This paper provides an understanding of some basic statistical properties of (WGDT-Ⅱ).It includes moments and maximum likelihood estimator. In addition to the above it imparts the insight to distribution function, survival rate, hazard rate and reverse hazard rate. The behavior of PDF, CDF, and Survival rate, Hazard rates and Reverse Hazard rates has been presented through various graphs by setting different values of parameters.

Open Access Original Research Article

A New Extended Generalized Inverse Exponential Distribution: Properties and Applications

Bashiru Omeiza Sule

Asian Journal of Probability and Statistics, Page 30-46
DOI: 10.9734/ajpas/2021/v11i230264

The quest by researchers in the area of distribution theory in proposing new models with greater flexibility has filled literature. On this note, we proposed a new distribution called the new extended generalized inverse exponential distribution with five positive parameters, which extends and generalizes the extended generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate, cumulative hazard rate function and odds functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to three real life data sets which show that the new extended generalized inverse exponential model provides greater flexibility and better fit than other competing models considered.

Open Access Original Research Article

Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

Yuqi Dou, Xingyu Liu

Asian Journal of Probability and Statistics, Page 47-57
DOI: 10.9734/ajpas/2021/v11i230265

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

Open Access Review Article

Time Series Analysis of Road Traffic Accidents in Ghana

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

Asian Journal of Probability and Statistics, Page 12-20
DOI: 10.9734/ajpas/2021/v11i230262

This study uses Time Series models to predict the annual traffic accidents in Ghana. The traffic accidents data spanning from January 1990 to December 2019 was used. The Box-Jenkins model building strategy was used. The Augmented Dickey Fuller (ADF) test showed that the accident data was stationary. Three ARMA models were suggested based on the ACF and PACF plots of the differenced series, these were ARMA (0,0), ARIMA (1,0), and ARMA (2,0). The model with the smallest corrected Akaike Information Criteria (AICs) and Bayesian Information Criteria (BIC) was chosen as the best model. The Ljung-Box statistics among others were used in assessing the quality of the model. ARMA (1,0) was the best model for the Ghana annual Traffic Accident data. The results showed that, from January to July, it would be difficult to make accurate estimates of the number of road incidents for the years leading up to 2020. This was due to the fact that the white noise process values were statistically independent at various times.