Message-ID: <x28z2o5b83.fsf@biostat.ku.dk>
Date: 2002-08-30T20:43:24Z
From: Peter Dalgaard
Subject: density() returns a density function that does not add up to 1
In-Reply-To: <3D6FD575.F67C78A9@labs.agilent.com>
Jonathan Li <jonqli at labs.agilent.com> writes:
> Thank you for the message. It helps a lot. I see where my method was
> wrong.
> Now another case:
>
> > dd <- c(rnorm(1000,0,1), rnorm(100, 100,1), rnorm(10, 1000,1))
> > ddd <- density(dd)
> > sum( diff(ddd$x)*ddd$y)
> [1] 2.856715
>
> If you add more extreme tails, the thing gets worse:
>
> > dd <- c(rnorm(1000,0,1), rnorm(100, 100,1), rnorm(10, 1000,1), rnorm(5, 5000,1))
> > ddd <- density(dd)
> > sum( diff(ddd$x) * ddd$y)
> [1] 13.90902
>
> I am not sure what is going on now?
You're trying to calculate and then integrate a very spiky density.
Try plotting it and then increase the number of points used to
approximate it:
> dd <- c(rnorm(1000,0,1), rnorm(100, 100,1), rnorm(10, 1000,1), rnorm(5, 5000,1))
> ddd <- density(dd,n=2^15)
> sum( diff(ddd$x) * ddd$y)
[1] 1.000014
Warning message:
longer object length
is not a multiple of shorter object length in: diff(ddd$x) * ddd$y
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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