[R] density > 1?

[Peter Dalgaard]

Johannes Elias wrote:
> 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?

This comes up every now and again. The real question is: Why do people
believe that densities should be probabilities? They're not, they denote
(differential) probability per unit on the x axis, and the denominator
can be small. The density _integrates_ to 1, so if e.g. it is
concentrated on (0, 0.5) if has to be at least 2 somewhere.

> Greetings,
> 
> Johannes
> 
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