Message-ID: <1BDAE2969943D540934EE8B4EF68F95FB22F4CBBE8@EXNSW-MBX03.nexus.csiro.au>
Date: 2009-03-02T12:34:45Z
From: Bill Venables
Subject: density > 1?
In-Reply-To: <49ABD0C6.9090808@hygiene.uni-wuerzburg.de>
Because densities are not probabilities. It is the area under the density curve that represents probability.
Example: the chi-squared density with 1 degree of freedom has a singularity at the zero and is unbounded. The area under the curve, however, is still 1.
(This is a distressingly common misconception. It is really not an R issue but a distribution theory issue.)
Bill Venables
________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of Johannes Elias [jelias at hygiene.uni-wuerzburg.de]
Sent: 02 March 2009 22:27
To: r-help at r-project.org
Subject: [R] density > 1?
Dear R-Gurus,
I wonder why 'density' values as shown in hist or plot(density(x)) are
sometimes over 1. How can that be?
Example
>hist(rnorm(1000,sd=.5),freq=FALSE)
The resulting plot shows density values below 1 on the y-axis. However,
>hist(rnorm(1000,sd=.1),freq=FALSE)
shows density values over 1.
How to interpret density values over 1?
Greetings,
Johannes
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