Solved – How to explain density() plots in R

density functionr

I am doing spectrum analysis. For two given bands, I find out the percentage utilization. I have percentage utilization on the x-axis and the estimated pdf on y-axis.

To make you follow how I got these plots

I load the measurement files which have the energy values
then I find the duty cycle per row as (I sweep once and then see how much spectrum is used) x<- apply(data, 1, duty_cycle, threshold)
and then I plot using plot(density(100*x)) so I get the % on the x axis.

SO the basic interpretation would be the maximum utilization is 40 %, although how is the y axis related.

How do I interpret the y-axis?

Best Answer

I always describe the "density" output as a "smooth histogram". The y-axis can't tell you much for a given point except a possible estimate of the continuous mode. The y-axis allows you to estimate event probabilities using the volume of the curve over certain regions. If you summed up the area (or integrated) between two values, you would arrive at an estimate of the probability of sampling a value between those two values in an independent replication of the data collection.

Related Solutions

Solved – Alternative to sieve / mosaic plots for contingency tables

The book you described sounds like, 'Visualizing Categorical Data,' Michael Friendly. The plot described in the 1st chapter that seems to match your request was described as a type of conceptual model for visualizing contingency table data (loosely described by the author as a dynamic pressure model with observational density), and can be seen in the google preview for Ch 1. The book is geared towards SAS users.

A paper on the topic is referenced here: www.datavis.ca/papers/koln/kolnpapr.pdf

'Conceptual Models for Visualizing Contingency Table Data,' Michael Friendly .

enter image description here

*incidentally, the author is also listed as one of the authors of the vcd package (as it was specifically inspired by his book mentioned above) -- maybe you could ask him directly if there's a simple modification to one of the built in functions that's not readily apparent.

** The coloring scheme seems to relate the color blue with positive deviations from independence, and red for negative deviations. Although the red scheme makes sense in that context, maybe it would have been more apt to have used green to represent positive deviations.

http://www.datavis.ca/papers/asa92.html

Solved – Relative density plots in R

Combining your own code with whuber's suggestions (but please bear in mind his warning), something like this might do the trick (untested):

xmin<-min(data$x)
xmax<-max(data$x)
n<-1000
Adens<-density(data[cl=="A"]$x), from=xmin, to=xmax, n=n)
Totdens<-density(data$x, from=xmin, to=xmax, n=n)

# Because each density by default has a total area of 1, rescale the y-values of Adens 
# such that its area represents the actual proportion of the A-class. Then, plot the
# ratio between both densities.
Aprop <- length(data[cl=="A"]$x)/length(data$x)
plot(Adens$x, Aprop*Adens$y/Totdens$y, type="l")

Does that work for you?

Best Answer

Related Solutions

Solved – Alternative to sieve / mosaic plots for contingency tables

Solved – Relative density plots in R

Related Question