[R] density > 1?

[Eik Vettorazzi]

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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>   

-- 
Eik Vettorazzi
Institut für Medizinische Biometrie und Epidemiologie
Universitätsklinikum Hamburg-Eppendorf

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