# [R] Density function: Area under density plot is not equal to 1. Why?

Albyn Jones jones at reed.edu
Thu Sep 8 19:03:17 CEST 2011

```Look at

area <- sum(a\$y)*(a\$x[1]-a\$y[2])

The problem appears to be "a\$x[1]-a\$y[2]"; that is not the length of
the base of an approximating rectangle, whatever it is :-)

albyn

On Thu, Sep 08, 2011 at 11:36:23AM -0400, Gonçalo Ferraz wrote:
> Hi, I have a vector 'data' of 58 probability values (bounded between 0 and 1) and want to draw a probability density function of these values. For this, I used the commands:
>
> data <- runif(58)
>
> a <- density(data, from=0, to=1)
> plot(a, type="l",lwd=3)
>
> But then, when I try to approximate the area under the plotted curve with the command:
>
> area <- sum(a\$y)*(a\$x[1]-a\$y[2])
>
> I get an area that is clearly smaller than 1.
>
> Strangely, if I don't bound the density function with 'to=0,from=1' (which is against my purpose because it extends the pdf beyond the limits of a probability value), I get an area of 1.000. This suggests that I am computing the area well, but using the density function improperly.
>
> Why is this happening? Does anyone know how to constrain the density function while still getting a true pdf (summing to 1 under the curve) at the end? Should I use a different function? I read through the density function notes but could not figure out a solution.
>
> Thank you!
>
> Gonçalo
>
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--
Albyn Jones
Reed College
jones at reed.edu

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