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

Johannes,

Well density is not like probability

In histogram with density the area is equal de probability 

in you example

set.seed(123)
hist(rnorm(1000,sd=.1),freq=FALSE)

The interval of -0.05 and 0 have density=4 but a probability of number
in this interval is 4*.05=.2

the fact 

set.seed(123)
hist(rnorm(1000,sd=.1),freq=FALSE)$density
[1] 0.09999998 0.28000000 0.94000000 1.98000000 2.60000000 4.00000000
[7] 4.04000000 2.92000000 1.66000000 0.92000000 0.44000000 0.10000000
[13] 0.02000000

set.seed(123)
sum(hist(rnorm(1000,sd=.1),freq=FALSE)$density)
[1] 1


So the sum of probability is 1 but the sum of density 20

Bernardo Rangel Tura, M.D,MPH,Ph.D
National Institute of Cardiology
Brazil