3,060 research outputs found
Analyzing Taguchi's experiments using GLIM with inverse Gaussian distribution.
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
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
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
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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