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Aimed at researchers across the social sciences, this book explains the logic behind the Monte Carlo simulation method and demonstrates its uses for social and behavioural research.
Findings and conclusions. The study revealed that the KS-2 test is smaller than the MW test in comparisons of the type I error rates in unequal sample sets. The MW test had slightly more statistical power the KS-2 test under the condition of small and equal-sized samples. Moreover, when population variances vary between two samples, the KS-2 test has more statistical power than the MW test. Furthermore, the power of the KS-2 test exceeded the power of the MW test in large sample settings when either one of the following conditions existed: (1) The difference in the Skewness ratoss in populations between the two samples was more than 0.5 with the same kurtosis and variance. (2) The difference in the Kurtosis ratios in populations between the two samples was more than 2.0 with the same skewness and variance. Theoretical and practical implications, limitations of the study, are discussed, as well as recommendations for future research.
Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the ``curse of dimensionality'', which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability. The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.