Comparative Analysis of the Powers the Two-Sample Kolmogorov-Smirnov and Anderson-Darling Tests Under Various Alternatives
In this paper we conduct a comparative analysis of the powers of the two-sample Kolmogorov–Smirnov and Anderson–Darling tests under various alternatives using simulation. We consider two examples. In the first example the alternatives to the standard normal distribution are the distributions of the so-called contaminated normal model. We study the influence of a small contamination with a positive shift on the powers of the test. In the second example the alternatives are the logistic and the Laplace distributions, which are symmetric and differ in shape from the normal distribution having a larger kurtosis coefficient and heavier tails.
We study the power of the two-sample Anderson–Darling test for fixed alternatives, when one sample is drawn from the standard normal distribution and the other is a mixture of two normal distributions. Using the modeling we study the behavior of the power function depending on the proportion of contamination for different sample sizes. For the same alternatives we compare the powers of Anderson–Darling and Kolmogorov–Smirnov tests. Similar results are obtained for the trimmed samples.
The paper proposes a method of multicriteria optimization under interval stochastic uncertainty of estimates given by the subject for the relative importance of one criterion over the other and the different alternatives to each other for each criterion. The method is an extension of the deterministic Analytic Hierarchy Process (AHP) for multicriteria optimization. It is use deterministic point estimates of the importance of criteria and alternatives for each criterion . While deterministic AHP allows to select the best alternative by a point maximum value of a global priority in the developed article interval stochastic AHP the global priorities are interval, making it difficult to make the best decision . To select the best interval alternative in this article introduce two criteria, whose values are maximized. The first criterion corresponds to the maximum of the lower and upper bounds of the intervals of global priorities of alternatives. The second criteria is the maximum of interval stability of alternatives. Application of the proposed approach is illustrated by a specific example. Also a comparison with the results obtained on the basis of interval arithmetic, show the failure of the latter, carried out.
Specific features of strategic decision making include a bulk of significant factors, availability of semi-structured and unstructured data, as well as incompleteness of source information. In such conditions, for assessment and selection of strategic initiatives an expert approach seems applicable, perhaps, in combination with traditional methods of management accounting and investment appraisal. An important aspect of strategic decision making is modeling of problem situations, which represent possible future conditions of external environment. Due to different approaches to problem situations modeling and diversity of decision making methods, multivariate processing of expert estimates seems reasonable. For appropriate calculations, application of special information systems is recommended. The aim of the research is to develop an approach to strategic decision making, including modeling of problem situations and multivariate processing of expert estimates, using appropriate decision making methods and information systems. During problem situations modeling (relying on factors of external environment that are material for decision making), it is considered that such factors may be either independent, of depended from each other. As one of the techniques of problem situations probabilities assessment, the method of Analytic Hierarchy Process (AHP) is applicable. Regarding multivariate processing of expert estimates, the methods applicable in the conditions of risk (when probabilities of problem situations are known) or uncertainty (when assessment of probabilities is not possible) are considered in the paper. The proposed recommendations are illustrated by the example of the task of selecting the mode of overseas market entry for a manufacturing company. Processing of source information relies on four different decision making methods; one of them is applied in the conditions of risk, and four – in uncertain environment. Appropriate calculations are executed using Expert Decision Support System (EDSS) software.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.