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An Analysis of the Alias Method for Discrete Random-Variate Generation

J. Cole Smith, Sheldon H. Jacobson
2005 INFORMS journal on computing  
The alias method is an efficient method to generate random variates from a discrete probability distribution.  ...  T his paper introduces and studies an optimization problem related to the alias method for discrete randomvariate generation.  ...  The authors thank the associate editor and two anonymous reviewers for their constructive and insightful suggestions.  ... 
doi:10.1287/ijoc.1030.0063 fatcat:z5jaexjfeff4pmk2dx7lhdvas4

Sampling from the exponential distribution using independent Bernoulli variates

David B. Thomas, Wayne Luk
2008 2008 International Conference on Field Programmable Logic and Applications  
This paper shows that each bit of a fixed-point exponential random variate is an independent Bernoulli variate, allowing the bits to be generated in parallel.  ...  The method is particularly useful for very high performance applications, as extremely high-quality 36-bit exponential variates can be generated at 600MHz in the Virtex-4 architecture, using just 880 slices  ...  Fig. 5 . 5 Building an alias table for a discrete distribution. Fig. 6 . 6 Alias-table generation architecture. Table 1. Generator parametrisations used in the evaluation.  ... 
doi:10.1109/fpl.2008.4629938 dblp:conf/fpl/ThomasL08 fatcat:lfgwc4igvfdarh5r45zb3dcwmq

Page 1104 of Mathematical Reviews Vol. , Issue 81C [page]

1981 Mathematical Reviews  
Authors’ summary: “The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution.  ...  Kronmal, Richard A.; Peterson, Arthur V., Jr. 81c:65010 On the alias method for generating random variables from a discrete distribution. Amer. Statist. 33 (1979), no. 4, 214-218.  ... 

Random Process Generation [chapter]

2011 Handbook of Monte Carlo Methods  
Also the common discrete distributions will receive some attention, probably in the form of extending the use of the acceptance/rejection algorithm to the discrete case and extending the alias method of  ...  variate generation to allow for countably infinite ranges of the random variables.  ... 
doi:10.1002/9781118014967.ch5 fatcat:tviic4cdebfizfgupkt3qttjoa

Rejection-inversion to generate variates from monotone discrete distributions

W. Hörmann, G. Derflinger
1996 ACM Transactions on Modeling and Computer Simulation  
It can be used to generate variates from the tails of most standard discrete distributions.  ...  Using rejection-inversion and a squeeze, a simple universal method for a large class of monotone discrete distributions is developed.  ...  Acknowledgement: The authors thank the referees and the area editor for their useful hints that substantially improved the presentation of the paper.  ... 
doi:10.1145/235025.235029 fatcat:ybaohpelezh3vjlc5rmgr6qrxu

Fast algorithms for generating discrete random variates with changing distributions

Sanguthevar Rajasekaran, Keith W. Ross
1993 ACM Transactions on Modeling and Computer Simulation  
In this paper we present algorithm for discrete random variate generation that take an expected O(1) time to generate each variate.  ...  In this paper we present algorithms for discrete random variate generation that take an expected O(1) time to generate each variate.  ...  Introduction The problem of generating a nonuniform discrete random variate is fundamental to simulation of any discrete event stochastic system.  ... 
doi:10.1145/151527.151529 fatcat:wz5kbiplwzbd7j7mhkc2f4bd3m

A note on a universal random variate generator for integer-valued random variables [article]

Lucio Barabesi, Luca Pratelli
2012 arXiv   pre-print
The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables.  ...  In addition, the method is suitable for the computer generation of integer-valued random variables which display closed-form characteristic functions, but do not possess a probability function expressible  ...  However, the inversion method generally produces quite inefficient algorithms and the alias method is suited for random variables taking values on a finite subset of integers.  ... 
arXiv:1211.0815v1 fatcat:bo56v6yefre65a7klyojlawphe

Page 5 of Applied Mechanics Reviews Vol. 14, Issue 1 [page]

1961 Applied Mechanics Reviews  
class of methods is alias-free, and display several alias-free mem- bers of this class.  ...  In addition to examining the problem with some generality, reviewer believes that the alias-free methods presented should be useful in practice.  ... 

Systematic errors in the measurement of power spectral density

Chris A. Mack
2013 Journal of Micro/Nanolithography  
Using both analytical expressions and numerical simulations for the measurement of the PSD of line-edge roughness, four sources of systematic errors are evaluated: aliasing, leakage, averaging, and image  ...  Measurement of the power spectral density (PSD) of a rough surface or a feature involves large random and systematic errors.  ...  Here, the Thorsos method 14,15 was used to generate random rough edges with a Gaussian distribution and correlation behavior determined by the Palasantzas PSD.  ... 
doi:10.1117/1.jmm.12.3.033016 fatcat:z5kgjq3kfrg3tkvtgigrovphom

jPhase

Juan F. Pérez, Germán Riaño
2006 Proceeding from the 2006 workshop on Tools for solving sturctured Markov chains - SMCtools '06  
Particularly, it has a general implementation of the alias method used to generate variates from discrete distributions [16] .  ...  The first one is the several use of discrete distributions to generate the variates, which can be done efficiently through the alias method [16] .  ... 
doi:10.1145/1190366.1190370 fatcat:lt5knxaelbgrxerdey22h4qy4q

Simulating Population Protocols in Sub-Constant Time per Interaction

Petra Berenbrink, David Hammer, Dominik Kaaser, Ulrich Meyer, Manuel Penschuck, Hung Tran, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
For our analysis, we consider plain arrays, binary search trees, and a novel Dynamic Alias Table data structure.  ...  We empirically and analytically analyze two classes of simulators for this model. First, we consider sequential simulators executing one interaction after the other.  ...  The algorithm by Vose [40] can generate an (original) alias table representation of such a discrete probability distribution D in O(k) time.  ... 
doi:10.4230/lipics.esa.2020.16 dblp:conf/esa/BerenbrinkHK0PT20 fatcat:mxosq3kbo5aq5m4btyze6jvix4

The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete Probability Distributions [article]

Feras A. Saad, Cameron E. Freer, Martin C. Rinard, Vikash K. Mansinghka
2020 arXiv   pre-print
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips.  ...  Empirical evaluations on a broad set of probability distributions establish that FLDR is 2x-10x faster in both preprocessing and sampling than multiple baseline algorithms, including the widely-used alias  ...  CONCLUSION This paper has presented the Fast Loaded Dice Roller, a new method for generating discrete random variates.  ... 
arXiv:2003.03830v2 fatcat:t6r3kgsqz5awfhck44k6kt24jm

Simulating Population Protocols in Sub-Constant Time per Interaction [article]

Petra Berenbrink and David Hammer and Dominik Kaaser and Ulrich Meyer and Manuel Penschuck and Hung Tran
2020 arXiv   pre-print
For our analysis, we consider plain arrays, binary search trees, and a novel Dynamic Alias Table data structure.  ...  In each time step, a pair of agents is selected uniformly at random to interact. In an interaction, agents update their states according to a common transition function.  ...  We would like to thank the Center for Scientific Computing, University of Frankfurt for making their HPC facilities available.  ... 
arXiv:2005.03584v1 fatcat:dwxl5y53lrcrznwpkvxf6cdmpy

George Fishman's Professional Career [chapter]

Christos Alexopoulos, David Goldsman, James R. Wilson
2009 International Series in Operations Research and Management Science  
Unsure of his commitment to engineering, he took a leave of absence in November 1956 and spent the next ten months working for the Whiting Milk Company in Charlestown, Massachusetts.  ...  We give special emphasis to George's remarkable accomplishments in helping to lay the foundation for the field of computer simulation and advancing that field over the past five decades.  ...  The book then presents an encyclopedic discussion on random variate generation techniques.  ... 
doi:10.1007/b110059_1 fatcat:i5rsjgeuyfcf7fqogmx3wkmecq

Parallel Weighted Random Sampling

Lorenz Hübschle-Schneider, Peter Sanders, Michael Wagner
2019 European Symposium on Algorithms  
ACM Subject Classification Theory of computation → Sketching and sampling; Theory of computation → Parallel algorithms; Theory of computation → Data structures design and analysis Supplement Material The  ...  Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known.  ...  Different PEs have to draw the same random variates for the same interior node of the tree. This can be achieved by seeding a pseudo-random number generator with an ID of this node.  ... 
doi:10.4230/lipics.esa.2019.59 dblp:conf/esa/Hubschle-Schneider19 fatcat:ilqbdd4vsnda7kvwo7j3xzc7ly
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