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

[Liaw, Andy]

Note that Tony did say "crude".  For your second example, try

  ddd <- density(dd, n=2^16)

That, hopefully, gives you enough clue.

(What exactly are you trying to do, anyway?  If the kernel used is an actual
pdf, as is case with all the kernel types in density(), I think, then the
estimated density is guaranteed to be a true density, since it's just an
n-component mixture of the kernels.  There's no need to use crude numerical
method to check the integral.)

Andy


> -----Original Message-----
> From: Jonathan Li [mailto:jonqli at labs.agilent.com]
> Sent: Friday, August 30, 2002 4:29 PM
> To: rossini at u.washington.edu
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] density() returns a density function that 
> does not add
> up to 1
> 
> 
> 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 
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> unpredictable.)
> 
> -- 
> Jonathan Q. Li, PhD
> Agilent Technologies Laboratory
> Palo Alto, California, USA
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