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22
NonUniform Random Variate Generation
, 1986
"... Abstract. This is a survey of the main methods in nonuniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various ..."
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Cited by 620 (21 self)
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Abstract. This is a survey of the main methods in nonuniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.
A Monte Carlo Approach to Nonnormal and Nonlinear StateSpace Modeling
, 1992
"... this article then is to develop methodology for modeling the nonnormality of the ut, the vt, or both. A second departure from the model specification ( 1 ) is to allow for unknown variances in the state or observational equation, as well as for unknown parameters in the transition matrices Ft and Ht ..."
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Cited by 126 (14 self)
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this article then is to develop methodology for modeling the nonnormality of the ut, the vt, or both. A second departure from the model specification ( 1 ) is to allow for unknown variances in the state or observational equation, as well as for unknown parameters in the transition matrices Ft and Ht. As a third generalization we allow for nonlinear model structures; that is, X t = ft(Xtl) q Ut, and Yt = ht(xt) + vt, t = 1, ..., n, (2) whereft( ) and ht(. ) are given, but perhaps also depend on some unknown parameters. The experimenter may wish to entertain a variety of error distributions. Our goal throughout the article is an analysis for general statespace models that does not resort to convenient assumptions at the expense of model adequacy
Subordinated AdvectionDispersion Equation for Contaminant Transport
 Water Resour. Res
, 2000
"... A mathematical method called subordination broadens the applicability of the classical advectiondispersion equation for contaminant transport. In this method the time variable is randomized to represent the operational time experienced by different particles. In a highly heterogeneous aquifer th ..."
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Cited by 9 (5 self)
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A mathematical method called subordination broadens the applicability of the classical advectiondispersion equation for contaminant transport. In this method the time variable is randomized to represent the operational time experienced by different particles. In a highly heterogeneous aquifer the operational time captures the fractal properties of the medium. This leads to a simple, parsimonious model of contaminant transport that exhibits many of the features (heavy tails, skewness, and nonFickian growth rate) typically seen in real aquifers. We employ a stable subordinator that derives from physical models of anomalous diffusion involving fractional derivatives. Applied to a onedimensional approximation of the MADE2 data set, the model shows excellent agreement.
A triptych of discrete distributions related to the stable law
, 1993
"... We derive useful distributional representations for three discrete laws: the discrete stable distribution of Steutel and Van Harn, the discrete Linnik distribution introduced by Pakes, and a distribution of Sibuya. These representations may be used to obtain simple uniformly fast random variate gen ..."
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Cited by 8 (0 self)
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We derive useful distributional representations for three discrete laws: the discrete stable distribution of Steutel and Van Harn, the discrete Linnik distribution introduced by Pakes, and a distribution of Sibuya. These representations may be used to obtain simple uniformly fast random variate generators.
Methods For Generating Random Variates With Polya Characteristic Functions
, 1984
"... Polya has shown that real even continuous functions that are convex on (0,oo), 1 for t  0, and decreasing to 0 as t, o are characteristic functions. Dugu6 and Girault (1955) have shown that the corresponding random variables are distributed as Y/Z where Y is a random variable with density (2) ( ..."
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Cited by 5 (3 self)
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Polya has shown that real even continuous functions that are convex on (0,oo), 1 for t  0, and decreasing to 0 as t, o are characteristic functions. Dugu6 and Girault (1955) have shown that the corresponding random variables are distributed as Y/Z where Y is a random variable with density (2) (sin(x/2)/(x/2)) 2, and Z is independent of Y and bas distribution function 1  + tk', t > 0. This property allows us to develop fast algorithms for this class of distributions. This is illustrated for the symmetric stable distribution, Linnik's distribution and a few other distributions. We pay special attention to the generation of Y.
Random variate generation for exponentially and polynomially tilted stable distributions
 ACM Transactions on Modeling and Computer Simulation 19, Article
, 2009
"... Abstract. We develop exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions. The algorithms, which generalize Kanter’s method, are uniformly fast over all choices of the tilting and stable parameters. The key to the solution is a new distributio ..."
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Cited by 3 (1 self)
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Abstract. We develop exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions. The algorithms, which generalize Kanter’s method, are uniformly fast over all choices of the tilting and stable parameters. The key to the solution is a new distribution which we call Zolotarev’s distribution. We also present a novel double rejection method that is useful whenever densities have an integral representation involving an auxiliary variable.
Some Bayesian perspectives on statistical modelling
, 1988
"... I would like to thank my supervisor, Professor A. F. M. Smith, for all his advice and encourage ..."
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Cited by 3 (2 self)
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I would like to thank my supervisor, Professor A. F. M. Smith, for all his advice and encourage
ON EXACT SIMULATION ALGORITHMS FOR SOME DISTRIBUTIONS RELATED TO JACOBI THETA FUNCTIONS
"... Abstract. We develop exact random variate generators for several distributions related to the Jacobi theta function. These include the distributions of the maximum of a Brownian bridge, a Brownian meander and a Brownian excursion, and distributions of certain first passage times of Bessel processes. ..."
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Cited by 2 (0 self)
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Abstract. We develop exact random variate generators for several distributions related to the Jacobi theta function. These include the distributions of the maximum of a Brownian bridge, a Brownian meander and a Brownian excursion, and distributions of certain first passage times of Bessel processes. The algorithms are based on the alternating series method. Furthermore, we survey various distributional identities and point out ways of dealing with generalizations of these basic distributions. Keywords and phrases. Random variate generation. Stable distribution. First passage time. Brownian motion. Rejection method. Simulation. Monte Carlo method. Expected time analysis. Probability inequalities.
Performance Of The Estimators Of Stable Law Parameters
"... : In this paper, we discuss the issue of estimation of the parameters of stable laws. We present an overview of the known methods and compare them on samples of different sizes and for different values of the parameters. Performance tables are provided. 1 Introduction The Central Limit Theorem, whi ..."
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Cited by 1 (1 self)
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: In this paper, we discuss the issue of estimation of the parameters of stable laws. We present an overview of the known methods and compare them on samples of different sizes and for different values of the parameters. Performance tables are provided. 1 Introduction The Central Limit Theorem, which offers the fundamental justification for approximate normality, points to the importance of ffstable (sometimes called stable) distributions: they are the only limiting laws of normalized sums of independent, identically distributed random variables. Gaussian distributions, the best known member of the stable family, have long been well understood and widely used in all sorts of problems. However, they do not allow for large fluctuations and are thus inadequate for modeling high variability. NonGaussian stable models, on the other hand, do not share such limitations. In general, the upper and lower tails of their distributions decrease like a power function. In literature, this is ofte...
Subordinated AdvectionDispersion Equation For Contaminant Transport
"... A mathematical method called subordination broadens the applicability of the classical advectiondispersion equation for contaminant transport. In this method, the time variable is randomized to represent the operational time experienced by different particles. In a highly heterogeneous aquifer, th ..."
Abstract

Cited by 1 (0 self)
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A mathematical method called subordination broadens the applicability of the classical advectiondispersion equation for contaminant transport. In this method, the time variable is randomized to represent the operational time experienced by different particles. In a highly heterogeneous aquifer, the operational time captures the fractal properties of the medium. This leads to a simple, parsimonious model of contaminant transport that exhibits many of the features (heavy tails, skewness, and nonFickian growth rate) typically seen in real aquifers. We employ a stable subordinator that derives from physical models of anomalous diffusion involving fractional derivatives. Applied to the MADE2 data set, the model shows excellent agreement. 1. INTRODUCTION The traditional advectiondispersion equation is a standard model for contaminant transport. The concentration profile for an ensemble of particles governed by this model will Baeumer et al., Subordinated AdvectionDispersion Equati...