article

Inverting the symmetrical beta distribution

Authors:

Pierre L'Ecuyer,

Richard SimardAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 32, Issue 4

Pages 509 - 520

https://doi.org/10.1145/1186785.1186786

Published: 01 December 2006 Publication History

Abstract

We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function, and its inverse is found via Newton's method. This algorithm can be used to generate beta random variates by inversion and is much faster than currently available general inversion methods for the beta distribution. It turns out to be very useful for generating gamma processes efficiently via bridge sampling.

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L'Ecuyer, P. 2004. Quasi-Monte Carlo methods in finance. In Proceedings of the Winter Simulation Conference, R. G. Ingalls et al., eds. IEEE Press, Piscataway, NJ.]]

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Cited By

Xiang JWang X(2022)Quasi-Monte Carlo simulation for American option sensitivitiesJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114268413(114268)Online publication date: Oct-2022
https://doi.org/10.1016/j.cam.2022.114268
Beentjes C(2021)Optimising Poisson bridge constructions for variance reduction methodsMonte Carlo Methods and Applications10.1515/mcma-2021-209027:3(249-275)Online publication date: 1-Jun-2021
https://doi.org/10.1515/mcma-2021-2090
Xiang JWang X(2020)Primal–dual quasi-Monte Carlo simulation with dimension reduction for pricing American optionsQuantitative Finance10.1080/14697688.2020.1753884(1-20)Online publication date: 18-May-2020
https://doi.org/10.1080/14697688.2020.1753884
Show More Cited By

Index Terms

Inverting the symmetrical beta distribution
1. Computing methodologies
  1. Modeling and simulation
2. Mathematics of computing
  1. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 32, Issue 4

December 2006

145 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1186785

Issue’s Table of Contents

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 December 2006

Published in TOMS Volume 32, Issue 4

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Cited By

Xiang JWang X(2022)Quasi-Monte Carlo simulation for American option sensitivitiesJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114268413(114268)Online publication date: Oct-2022
https://doi.org/10.1016/j.cam.2022.114268
Beentjes C(2021)Optimising Poisson bridge constructions for variance reduction methodsMonte Carlo Methods and Applications10.1515/mcma-2021-209027:3(249-275)Online publication date: 1-Jun-2021
https://doi.org/10.1515/mcma-2021-2090
Xiang JWang X(2020)Primal–dual quasi-Monte Carlo simulation with dimension reduction for pricing American optionsQuantitative Finance10.1080/14697688.2020.1753884(1-20)Online publication date: 18-May-2020
https://doi.org/10.1080/14697688.2020.1753884
Sabino P(2020)Forward or backward simulation? A comparative studyQuantitative Finance10.1080/14697688.2020.1741668(1-14)Online publication date: 7-Apr-2020
https://doi.org/10.1080/14697688.2020.1741668
Abdellah AL'Ecuyer PPuchhammer FSon YHaas P(2019)Array-RQMC for option pricing under stochastic volatility modelsProceedings of the Winter Simulation Conference10.5555/3400397.3400433(440-451)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3400397.3400433
Abdellah AL'Ecuyer PPuchhammer F(2019)Array-RQMC for Option Pricing Under Stochastic Volatility Models2019 Winter Simulation Conference (WSC)10.1109/WSC40007.2019.9004819(440-451)Online publication date: Dec-2019
https://doi.org/10.1109/WSC40007.2019.9004819
L’Ecuyer P(2018)Randomized Quasi-Monte Carlo: An Introduction for PractitionersMonte Carlo and Quasi-Monte Carlo Methods10.1007/978-3-319-91436-7_2(29-52)Online publication date: 4-Jul-2018
https://doi.org/10.1007/978-3-319-91436-7_2
Shanmugam RChattamvelli R(2016)ReferencesStatistics for Scientists and Engineers10.1002/9781119047063.refs(441-454)Online publication date: 29-Apr-2016
https://doi.org/10.1002/9781119047063.refs
Varghese B(2015)The hardware accelerator debateComputers and Electrical Engineering10.1016/j.compeleceng.2015.01.01246:C(157-175)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1016/j.compeleceng.2015.01.012
Varghese BRau-Chaplin A(2013)Accounting for secondary uncertaintyProceedings of the 6th Workshop on High Performance Computational Finance10.1145/2535557.2535562(1-10)Online publication date: 18-Nov-2013
https://dl.acm.org/doi/10.1145/2535557.2535562
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