Liaw, Andy
2004-Dec-02 13:33 UTC
[R] A somewhat off the line question to a log normal distrib
> From: Robin Hankin > > [stuff about the CLT deleted] > > > > > So you can use R usefully to eveluate general statisical > > issues of this kind! > > > > absolutely! R is excellent for this sort of thing. I use it for > teaching stats all the time. > I'd say that without a tool like R you cannot learn statistics. > > > Consider an exponential distribution, which is very skewed. > > f <- function(n){mean(rexp(n))} > > then f(10) gives the mean of 10 independent exponentially distributed > random > variables. Then > > hist(replicate(10000,f(10))) > > gives us a histogram of 10000 observations of a variable that > is itself > the mean of 10 exponential variables. It still looks a bit > skew to me. > Try 100 exponential variables: > > hist(replicate(10000,f(100))) > > Still a tiny bit skew. > > > hist(replicate(1000,f(1000))) > which is indistinguishable from a Gaussian. > > > So as n -> infinity, the CLT kicks in. But here 100 is a bit > less than > infinity and 1000 ~= infinity. > > It's one thing to know a theoretical result, it's quite another to > verify it numerically.... but one needs to be careful when going the other direction: It's dangerous to take what is seen in numerical experiments as the `truth', without verifying it more rigorously. Andy> Kia Ora > > > Best wishes, > > Ted. > > > > > > -------------------------------------------------------------------- > > E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk> > > Fax-to-email: +44 (0)870 094 0861 [NB: New number!] > > Date: 02-Dec-04 Time: 11:30:01 > > ------------------------------ XFMail ------------------------------ > > > > ______________________________________________ > > R-help at stat.math.ethz.ch mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide! > > http://www.R-project.org/posting-guide.html > > > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > >
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