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1	Generating Generalized Inverse Gaussian Random Variates by Fast Inversion Leydold, Josef, Hörmann, Wolfgang January 2009 (has links) (PDF) We demonstrate that for the fast numerical inversion of the (generalized) inverse Gaussian distribution two algorithms based on polynomial interpolation are well-suited. Their precision is close to machine precision and they are much faster than the bisection method recently proposed by Y. Lai. / Series: Research Report Series / Department of Statistics and Mathematics MSC 65C05, 65C10
2	Generating Generalized Inverse Gaussian Random Variates Hörmann, Wolfgang, Leydold, Josef January 2013 (has links) (PDF) The generalized inverse Gaussian distribution has become quite popular in financial engineering. The most popular random variate generator is due to Dagpunar (1989). It is an acceptance-rejection algorithm method based on the Ratio-of-uniforms method. However, it is not uniformly fast as it has a prohibitive large rejection constant when the distribution is close to the gamma distribution. Recently some papers have discussed universal methods that are suitable for this distribution. However, these methods require an expensive setup and are therefore not suitable for the varying parameter case which occurs in, e.g., Gibbs sampling. In this paper we analyze the performance of Dagpunar's algorithm and combine it with a new rejection method which ensures a uniformly fast generator. As its setup is rather short it is in particular suitable for the varying parameter case. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics RVK QH 230, SK 820, SK 800, SK 835
3	A Study of Gamma Distributions and Some Related Works Chou, Chao-Wei 11 May 2004 (has links) Characterization of distributions has been an important topic in statistical theory for decades. Although there have been many well known results already developed, it is still of great interest to find new characterizations of commonly used distributions in application, such as normal or gamma distribution. In practice, sometimes we make guesses on the distribution to be fitted to the data observed, sometimes we use the characteristic properties of those distributions to do so. In this paper we will restrict our attention to the characterizations of gamma distribution as well as some related studies on the corresponding parameter estimation based on the characterization properties. Some simulation studies are also given. renewal process. characterization constancy of regression gamma distribution mean squared error power of hypothesis testing Laplace transform method of moments generalized inverse Gaussian Poisson process inverse Gaussian distribution Beta distribution bivariate gamma distribution parameter estimation change of measure

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