Message-ID: <Pine.LNX.4.31.0208302121180.16296-100000@gannet.stats>
Date: 2002-08-30T20:28:46Z
From: Brian Ripley
Subject: User error (was [R] density() returns a density function that does not add up to 1)
In-Reply-To: <3D6FCC84.F16D2B3B@labs.agilent.com>
On Fri, 30 Aug 2002, Jonathan Li wrote:
> I ran into this curious problem:
(or, I did something silly)
> > d <- rnorm(100)
> > d.density <- density(d)
> > sum( d.density$x * d.density$y)
> [1] 2.517502
>
> Admittedly the method of computing the mass under the density curve at
> line 3 is crude.
(and got a nonsensical answer)
> But 2.5 is pretty far from 1, the value it should be.
>
> I tried a few other dataset and got similar result. Am I missing
> something obvious?
> Or is the return of density() not supposed to be normalized?
I think you intended
sum( unique(diff(d.density$x)) * d.density$y )
Your sum is 512x the estimate of E(X).
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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