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

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From: A.J. Rossini (rossini@blindglobe.net)
Date: Sat 31 Aug 2002 - 06:05:08 EST 

Message-id: <87r8ggi03v.fsf@jeeves.blindglobe.net>

>>>>> "jonathan" == Jonathan Li <jonqli@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

I get 6.5

    jonathan> Admittedly the method of computing the mass under the density curve at
    jonathan> line 3 is crude.

It's actually wrong. You aren't computing an integral, you need the
the approximate area under d.density$y[i], NOT the value of the X
axis.

    jonathan> But 2.5 is pretty far from 1, the value it should be.

nope.

    jonathan> I tried a few other dataset and got similar result. Am I missing
    jonathan> something obvious?
    jonathan> Or is the return of density() not supposed to be normalized?

You just need to integrate properly. You are attempting Riemann
integration, but need to change things a bit.

best,
-tony 

-- 
A.J. Rossini				Rsrch. Asst. Prof. of Biostatistics
U. of Washington Biostatistics		rossini@u.washington.edu	
FHCRC/SCHARP/HIV Vaccine Trials Net	rossini@scharp.org
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