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

Gonçalo Ferraz gferraz29 at gmail.com
Thu Sep 8 17:36:23 CEST 2011

```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

```