Min-max approach for comparison of univariate normality tests

Comparison of normality tests based on absolute or average powers are bound to give ambiguous results, since these statistics critically depend upon the alternative distribution which cannot be specified. A test which is optimal against a certain type of alternatives may perform poorly against other alternative distributions. Thus, an invariant benchmark is proposed in the recent normality literature by computing Neyman-Pearson tests against each alternative distribution. However, the computational cost of this benchmark is significantly high, therefore, this study proposes an alternative approach for computing the benchmark. The proposed min-max approach reduces the calculation cost in terms of computing and estimating the Neyman-Pearson tests against each alternative distribution. An extensive simulation study is conducted to evaluate the selected normality tests using the proposed methodology. The proposed min-max method produces similar results in comparison with the benchmark based on Neyman-Pearson tests but at a low computational cost.

Modeling Carbon Emissions of Alternative Distribution Network Designs for Seaport to Demand Center Just in Time Delivery

This chapter presents a decision support tool that can be used to evaluate the level of carbon emission and duration of delivery time for alternative distribution systems charged with just-in-time product delivery. An Excel-based transportation model is solved using linear programming to model transport truck carbon emissions and delivery time for a product landed at seaports in the United States and transported to meet customer demand at inland locations under stochastic demand conditions. The alternative network designs examined provide insights as to the viability of the optimal network design as determined by the transportation model. The model is illustrated using simulated demand scenarios and the robustness of the solution methodology is examined using a sensitivity analysis.

Exploring Alternative Distribution Channels of Agricultural Products

Fresh fruits and vegetables constitute the basis of many people's daily nutrition habits and different distribution systems have been developed to cover daily supply needs. Important components of alternative distribution channels among others are high quality, high standards and consumer-producer trust. Although numerous studies have been conducted on alternative types of distribution channels, there is a lack of research on consumer behaviour towards these ways of distribution. The aim of this article is to identify consumer attitudes and preferences towards alternative agricultural distribution channels regarding fresh fruits and vegetables. In addition, this article contributes to the understanding of consumer behaviour, by pointing out the factors that affect the final purchase of agricultural products.

Pyramidal Distribution: An Alternative Distribution for Bivariate Uniformity Test Power Comparison

The purpose of the multi-dimensional uniformity test is to check whether the underlying probability distribution, from which a random sample is drawn, differs from the multi-dimensional uniform distribution. The multi-dimensional uniformity test has applications in various fields such as biology, astronomy and computer science. Various statistical tests have been proposed for the multivariate uniformity. As a special case, the bivariate statistic test is discussed in this paper. To evaluate the performance of the uniformity tests, power comparison is the technique for selecting appropriate statistical test. The Monte Carlo simulations usually used to compare the power of the tests. Berrendero, Cuevas and Vazquez-Grande proposed a distance-to-boundary test, which was one of the latest published statistical tests for multi-dimensional uniformity [J. R. Berrendero, A. Cuevas and F. Vazquez-Grande, Testing multivariate uniformity: The distance-to-boundary method, Canad. J. Stat. 34 (2006) 693–707]. Chen and Hu proposed another test for multivariate uniformity [Z. Chen and T. Hu, Statistical test for bivariate uniformity, Adv. Stat. 2014 (2014) 740831]. Power comparison was conducted to compare these tests. In order to get more convincing power comparison results, more alternative distributions should be used when power study is conducted. This paper proposes a new bivariate distribution, named the pyramidal distribution, with support set [Formula: see text]. This distribution is quite flexible so that it can be used to produce different shapes of bivariate distributions. Because of that, the proposed distribution can be used as an alternative distribution in power comparison for bivariate uniformity test.