R help - Mar 2010 - Is this a bug (or a feature) in hist(x)$density ??

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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On Mar 13, 2010, at 3:39 PM, Tal Galili wrote:
> Hi all,
>
> A friend send me a question on why does this:
>
> x<-rpois(100,1)
> sum( hist(x)$density )
>
> Gives out "2"
Yes. And...
 > hist(x)$breaks
[1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
>
> 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 ?
>
I do think that neither you nor your friend understand densities.

-- 
David.

David Winsemius, MD
West Hartford, CT

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
> 
> 
> 
> ----------------Contact
> Details:-------------------------------------------------------
> Contact me: Tal.Galili at gmail.com |  972-52-7275845
> Read me: www.talgalili.com (Hebrew) | www.biostatistics.co.il (Hebrew) |
> www.r-statistics.com (English)
>
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> 
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