Message-ID: <49ABD49B.7030406@uke.uni-hamburg.de>
Date: 2009-03-02T12:44:11Z
From: Eik Vettorazzi
Subject: density > 1?
In-Reply-To: <49ABD0C6.9090808@hygiene.uni-wuerzburg.de>
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 f?r Medizinische Biometrie und Epidemiologie
Universit?tsklinikum Hamburg-Eppendorf
Martinistr. 52
20246 Hamburg
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