[R] density() returns a density function that does not add up to 1

[Jonathan Li]

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?
Thanks again!
Jonathan


"A.J. Rossini" wrote:
> 
> >>>>> "jonathan" == Jonathan Li <jonqli at labs.agilent.com> writes:
> 
>     jonathan> Dear R users,
>     jonathan> I ran into this curious problem:
> 
>     >> d <- rnorm(100)
>     >> d.density <- density(d)
>     >> sum( d.density$x * d.density$y)
>     jonathan> [1] 2.517502
> 
> whoops, you probably want something like:
> 
> > sum( diff(d.density$x) * d.density$y)
> [1] 1.000950
> 
> instead, for a crude integration (and yes, it throws a warning).
> 
> --
> A.J. Rossini                            Rsrch. Asst. Prof. of Biostatistics
> U. of Washington Biostatistics          rossini at u.washington.edu
> FHCRC/SCHARP/HIV Vaccine Trials Net     rossini at scharp.org
> -------------- http://software.biostat.washington.edu/ ----------------
> FHCRC: M: 206-667-7025 (fax=4812)|Voicemail is pretty sketchy/use Email
> UW:   Th: 206-543-1044 (fax=3286)|Change last 4 digits of phone to FAX
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-- 
Jonathan Q. Li, PhD
Agilent Technologies Laboratory
Palo Alto, California, USA
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