# [R] Is this a bug (or a feature) in hist(x)\$density ??

Stephan Kolassa Stephan.Kolassa at gmx.de
Sat Mar 13 22:04:47 CET 2010

```Hi Tal,

basically, by summing over the (pointwise) density, you are
"approximating" the integral over the density (which should be around 1)
- but to really do a rectangular approximation, you will of course need
to multiply each function value by the width of the corresponding
rectangle. I'd recommend reading through Wikipedia's article on the
Riemann integral, you may be enlightened.
http://en.wikipedia.org/wiki/Riemann_integral

HTH,
Stephan

Tal Galili schrieb:
> Hi all,
>
> A friend send me a question on why does this:
>
> x<-rpois(100,1)
> sum( hist(x)\$density )
>
> Gives out "2"
>
> I tried this:
>
> sum( hist(x, freq =T)\$density )
>
> It didn't help.
>
> Then he came back with the following insight:
>
> # with breaks
> b<-c(0,0.9,1:8)
> sum(hist(x,breaks=b)\$density) # Much more then 2
> # but if we add weights according to the interval length
> sum(hist(x,breaks=b)\$density * diff(b))
> # it works
>
>
>
> What do you think ?
>
>
> Tal
>
>
>
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