[R] density > 1?

[Bill.Venables at csiro.au]

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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