[R] A random number from any distribution??
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Sun Dec 13 10:35:51 CET 2009
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.
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
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~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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