How to calculate the distance between two density functions

A similar question was posed and answered:

http://finzi.psych.upenn.edu/R/Rhelp02a/archive/119793.html

Two aspects needed to be addressed ... specifying the same domain, and  
getting the x-values to "line up" prior to the subtraction (or  
whatever function is desired).

What are you going to do when the two functions cross?

  d1 <- dnorm(seq(-2,2,by=.1))
  d2 <- dnorm(seq(-2,2,by=.1), mean=2)
  plot(seq(-2,2,by=.1),d1)
  lines(seq(-2,2,by=.1),d2)

---- or----

  d4 <- dnorm(seq(-4,4,by=.1))
  d5 <- dnorm(seq(-4,4,by=.1), sd=5)
  plot(seq(-4,4,by=.1),d4)
  lines(seq(-4,4,by=.1),d5)

David Winsemius
On Dec 5, 2008, at 8:59 AM, Chang Jia-Ming wrote:

> Dear all,
>
>  I wrote the following code to calculate the density functions for  
> two data
> sets, respectively.
>
>  den_str <-density(str_data$Similarity);
>  den_non_str <-density(nonstr_data$Similarity);
>
>  However, I would like to knowing the difference between den_str and
> den_non_str, that is, the difference between the region under the  
> curve of
> the den_str and the region under the curve of the den_non_str.
>
> How to do?
>
> Thank you for help.
>
> Jia-Ming
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org 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.

In general, comparing two continuous densities is difficult because they
can differ on a set of measure 0 (i.e., at a single point) and yet have
the same distribution function. 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Chang Jia-Ming
Sent: Friday, December 05, 2008 8:00 AM
To: r-help at r-project.org
Subject: [R] How to calculate the distance between two density functions

Dear all,

  I wrote the following code to calculate the density functions for two
data sets, respectively.

  den_str <-density(str_data$Similarity);
  den_non_str <-density(nonstr_data$Similarity);

  However, I would like to knowing the difference between den_str and
den_non_str, that is, the difference between the region under the curve
of the den_str and the region under the curve of the den_non_str.

 How to do?

 Thank you for help.

Jia-Ming


______________________________________________
R-help at r-project.org 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.

Dear all,

 I wrote the following code to calculate the density functions for two data
sets, respectively.

 den_str <-density(str_data$Similarity);
 den_non_str <-density(nonstr_data$Similarity);

 However, I would like to knowing the difference between den_str and
den_non_str, that is, the difference between the region under the curve of
the den_str and the region under the curve of the den_non_str.

One way of calculating the difference between two density functions
(or more general histograms), is the Earth Movers Distance
(e.g.http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/RUBNER/emd.htm
or http://en.wikipedia.org/wiki/Earth_Mover's_Distance ).
Dirk Eddelbuettel and myself are finalizing an implementation of it
and it will be available as soon as some licensing issues are sorted
out, which will be hopefully rather soon. If you don't want to wait
till the release, please drop either Dirk or myself an email and we
could mail you the package. As I said, the implementation is working
(I am using it in a research project at the moment), it is just that
the license is at the moment nonprofit research only.

Rainer

 How to do?

 Thank you for help.

Jia-Ming

       [[alternative HTML version deleted]]

______________________________________________
R-help at r-project.org 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.

Rainer M. Krug, PhD (Conservation Ecology, SUN), MSc (Conservation
Biology, UCT), Dipl. Phys. (Germany)

Centre of Excellence for Invasion Biology
Faculty of Science
Natural Sciences Building
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University of Stellenbosch
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