3,060 research outputs found

    Analyzing Taguchi's experiments using GLIM with inverse Gaussian distribution.

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    by Wong Kwok Keung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 50-52).Chapter 1. --- Introduction --- p.1Chapter 2. --- Taguchi's methodology in design of experiments --- p.3Chapter 2.1 --- System designChapter 2.2 --- Parameter designChapter 2.3 --- Tolerance designChapter 3. --- Inverse Gaussian distribution --- p.8Chapter 3.1 --- GenesisChapter 3.2 --- Probability density functionChapter 3.3 --- Estimation of parametersChapter 3.4 --- ApplicationsChapter 4. --- Iterative procedures and Derivation of the GLIM 4 macros --- p.21Chapter 4.1 --- Generalized linear models with varying dispersionChapter 4.2 --- Mean and dispersion models for inverse Gaussian distributionChapter 4.3 --- Devising the GLIM 4 macroChapter 4.4 --- Model fittingChapter 5. --- Simulation Study --- p.34Chapter 5.1 --- Generating random variates from the inverse Gaussian distributionChapter 5.2 --- Simulation modelChapter 5.3 --- ResultsChapter 5.4 --- DiscussionAppendix --- p.46References --- p.5

    Simulation techniques for generalized Gaussian densities

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    This contribution deals with Monte Carlo simulation of generalized Gaussian random variables. Such a parametric family of distributions has been proposed in many applications in science to describe physical phenomena and in engineering, and it seems also useful in modeling economic and financial data. For values of the shape parameter a within a certain range, the distribution presents heavy tails. In particular, the cases a=1/3 and a=1/2 are considered. For such values of the shape parameter, different simulation methods are assessed.Generalized Gaussian density, heavy tails, transformations of rendom variables, Monte Carlo simulation, Lambert W function

    Random numbers from the tails of probability distributions using the transformation method

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    The speed of many one-line transformation methods for the production of, for example, Levy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, is very high and satisfactory for most purposes. However, for the class of decreasing probability densities fast rejection implementations like the Ziggurat by Marsaglia and Tsang promise a significant speed-up if it is possible to complement them with a method that samples the tails of the infinite support. This requires the fast generation of random numbers greater or smaller than a certain value. We present a method to achieve this, and also to generate random numbers within any arbitrary interval. We demonstrate the method showing the properties of the transform maps of the above mentioned distributions as examples of stable and geometric stable random numbers used for the stochastic solution of the space-time fractional diffusion equation.Comment: 17 pages, 7 figures, submitted to a peer-reviewed journa

    Spatially Adaptive Stochastic Multigrid Methods for Fluid-Structure Systems with Thermal Fluctuations

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    In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic numerical methods are developed based on multigrid which allow for the efficient computation of both the hydrodynamic interactions in the presence of walls and the thermal fluctuations. The presented stochastic multigrid approach provides efficient real-space numerical methods for generating the required stochastic driving fields with long-range correlations consistent with statistical mechanics. The presented approach also allows for the use of spatially adaptive meshes in resolving the hydrodynamic interactions. Numerical results are presented which show the methods perform in practice with a computational complexity of O(N log(N))
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