Hi, I'm looking for a function to measure the dispersion of a set of values ranging from 0 to 1. This function should be 0 if all the values are evenly spaced within the interval and it should be > 0 if values are clustered. The more clustered the values are, the higher should the function be. An example: [0; 0.2; 0.4; 0.6; 0.8; 1] - function should be ~ 0 [0; 0.1; 0.1; 0.15; 1] - function should be > 1 This data comes from time-dependent observations recorded between a start time (0) and an end time (1). I want to find out which series are more clustered, i.e. less evenly distributed. I'm going to test Kurtosis for this but it doesn't seem to be the best tool for the job. As I understand, Kurtosis evaluates the "strength" of a single central peak. My data can have multiple peaks (clusters). Thanks in advance for your comments, -- S?rgio Nunes
S. Nunes wrote:> Hi, > > I'm looking for a function to measure the dispersion of a set of > values ranging from 0 to 1. > This function should be 0 if all the values are evenly spaced within > the interval and it should be > 0 if values are clustered. > The more clustered the values are, the higher should the function be. > > An example: > > [0; 0.2; 0.4; 0.6; 0.8; 1] - function should be ~ 0 > [0; 0.1; 0.1; 0.15; 1] - function should be > 1 > > This data comes from time-dependent observations recorded between a > start time (0) and an end time (1). > I want to find out which series are more clustered, i.e. less evenly > distributed. > > I'm going to test Kurtosis for this but it doesn't seem to be the best > tool for the job. > As I understand, Kurtosis evaluates the "strength" of a single central > peak. My data can have multiple peaks (clusters). >Hi Sergio, It sounds like what you want is the negative of the entropy. I'm not sure if there is a readymade function to calculate this, but someone else on the list might know. Jim
You could also look at the difference between your empirical distribution and the uniform distribution (something like Kolmogorov-Smirnov test). --- On Tue, 17/6/08, S. Nunes <snunes at gmail.com> wrote:> From: S. Nunes <snunes at gmail.com> > Subject: [R] Measuring dispersion > To: r-help at stat.math.ethz.ch > Received: Tuesday, 17 June, 2008, 7:56 PM > Hi, > > I'm looking for a function to measure the dispersion of > a set of > values ranging from 0 to 1. > This function should be 0 if all the values are evenly > spaced within > the interval and it should be > 0 if values are > clustered. > The more clustered the values are, the higher should the > function be. > > An example: > > [0; 0.2; 0.4; 0.6; 0.8; 1] - function should be ~ 0 > [0; 0.1; 0.1; 0.15; 1] - function should be > 1 > > This data comes from time-dependent observations recorded > between a > start time (0) and an end time (1). > I want to find out which series are more clustered, i.e. > less evenly > distributed. > > I'm going to test Kurtosis for this but it doesn't > seem to be the best > tool for the job. > As I understand, Kurtosis evaluates the > "strength" of a single central > peak. My data can have multiple peaks (clusters). > > Thanks in advance for your comments, > -- > S?rgio Nunes > > ______________________________________________ > 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.