Introducing Monte Carlo Methods with R [precision] | Xi'an's Og

Introducing Monte Carlo Methods with R [precision]

Doug Rivers, professor of Political Sciences in Stanford, kindly sent me this email yesterday night:

The 2nd displayed equation in section 2.1.2 on p. 44 is garbled (it might be interpreted as saying that U and X have the same distribution). I think you intended:

$P(U \leq u) = P[F(X) \leq u] = P[F^{-1}(F(X)) \leq F^{-1}(u)] = P[X \leq F^{-1}(u)] = F[F^{-1}(u)] = u$

And indeed we should have stated the implicit convention that u=F(x) before this equation, i.e.

$P(U \leq F(x))=P[F(X) \leq F(x)]=P[X \leq x]=F(x)$

(although U and X cannot be seen to have the same distribution as they live in different spaces).

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This entry was posted on January 17, 2011 at 1:13 pm and is filed under Books, R, Statistics with tags Introducing Monte Carlo Methods with R, typos. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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