density > 1?

Hi Johannes,
ist more a statistical issue. In short: densities are not probabilities! 
With a continuous random variable probability statements are typically 
over intervals not over points.
A density is bound to have an integral of 1 (and to be non-negative), 
nothing else.
Consider the uniform (0,0.5) distribution there the density is f(x)=2 
for all 0<=x<=0.5. This is a perfect probability density having all 
non-zero values > 1.

hth.

Johannes Elias schrieb:

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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