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On simulating a class of Bernstein polynomials

On Simulating a Class of Bernstein Polynomials VINEET GOYAL and KARL SIGMAN, Columbia University Given a black box that generates independent Bernoulli samples with an unknown bias p, we consider the problem of simulating a Bernoulli random variable with bias f ( p) (where f is a given function) using a nite (computable in advance) number of independent Bernoulli samples from the black box. We show that this is possible if and only if f is a Bernstein polynomial with coef cients between 0 and 1, and we explicitly give the algorithm. Our results differ from Keane and O ™Brien [1994] in that our goal is more modest/stringent, since we are considering algorithms that use a nite number of samples as opposed to allowing a random number (such as in acceptance rejection algorithms). Categories and Subject Descriptors: I.6.1 [Computing Methodologies]: Simulation and Modeling General Terms: Algorithms, Performance Additional Key Words and Phrases: Simulation, Bernstein polynomials ACM Reference Format: Goyal, V. and Sigman, K. 2012. On simulating a class of Bernstein polynomials. ACM Trans. Model. Comput. Simul. 22, 2, Article 12 (March 2012), 5 pages. DOI = 10.1145/2133390.2133396 http://doi.acm.org/10.1145/2133390.2133396 1. INTRODUCTION In this article, we consider the problem of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

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