On Simulating a Class of Bernstein Polynomials

被引：4

作者：

Goyal, Vineet ^{[1
]}

Sigman, Karl ^{[1
]}

机构：

[1] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA

来源：

ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION | 2012年 / 22卷 / 02期

关键词：

Simulation; Bernstein polynomials;

D O I：

10.1145/2133390.2133396

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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 finite (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 coefficients 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 finite number of samples as opposed to allowing a random number (such as in acceptance rejection algorithms).

引用

页数：5