ivan popivanov wrote:
Hello,
I have some data, and I want to generate random numbers following the distribution of this data (in other words, to generate a synthetic data set sharing the same stats as a given data set). Reading an old thread I found the following text:
If you can compute the quantile function of the distribution (i.e., the
inverse of the integral of the pdf), then you can use the probability
integral transform: If U is a U(0,1) random variable and Q is the quantile
function of the distribution F, then Q(U) is a random variable distributed
as F.
That sounds good, but is there a quick way to do this in R? Let's say my data is contained in "ee", I can get the quantiles using:
qq = quantile(ee, probs=(0,1,0.25))
0% 25% 50% 75% 100%
-0.2573385519 -0.0041451053 0.0004538924 0.0049276991 0.1037823292
Then I "know" how to use the above method to generate Q(U) (by looking up U in the first row, and then mapping it to a number using the second row), but is there an R function that does that? Otherwise I need to write my own to lookup the table.
Thanks in advance,
Ivan
Q <- approxfun(x,sort(ee)) with x=(0:(n-1))/(n-1) is your friend, I think.
Beware the details of the interpolation, though, in some variants you
end up reinventing the bootstrap. Also the fact that your generated
variables tend to be constrained to the range of ee should at least be
noted.
--
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c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
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~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
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