Transcription of 1 Acceptance-Rejection Method - Columbia …
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1 Acceptance-Rejection Method - Columbia …
Copyrightc 2007 by Karl Sigman1 Acceptance-Rejection MethodAs we already know, finding an explicit formula forF 1(y) for the cdf of a rvXwe wish togenerate,F(x) =P(X x), is not always possible. Moreover, even if it is, there may bealternative methods for generating a rv distributed asFthat is more efficient than the inversetransform Method or other methods we have come across. Here we present a very clever methodknown as theacceptance- rejection start by assuming that theFwe wish to simulate from has a probability density functionf(x); that is, the continuous case. Later we will give a discrete version too, which is very basic idea is to find an alternative probability distributionG, with density functiong(x),from which we already have an efficient algorithm for generating from ( , inverse transformmethod or whatever), but also such that the functiong(x) is close tof(x).
1 c Z ∞ f(y)dy = 1 c, where the last equality follows since f is a density function (hence by definition integrates to 1). Thus E(N) = c, the bounding constant, and we can now indeed see that it is desirable
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