Because densities are not probabilities. It is the area under the density curve that represents probability.
Example: the chi-squared density with 1 degree of freedom has a singularity at the zero and is unbounded. The area under the curve, however, is still 1. (This is a distressingly common misconception. It is really not an R issue but a distribution theory issue.) Bill Venables ________________________________________ From: [email protected] [[email protected]] On Behalf Of Johannes Elias [[email protected]] Sent: 02 March 2009 22:27 To: [email protected] Subject: [R] 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 ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
