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Question

I am trying to place 3 density functions in plot using

plot(density(all_noise),xlim=c(-1,1),ylim=c(0,10))
lines(density(max_nearby),col="blue")
lines(density(max_repeats),col="red")

and I got

Shouldn't the density value on the y axis be < 1? Are there better methods for superimposing kernel distributions?

str(density(all_noise))
List of 7
$ x        : num [1:512] -0.629 -0.626 -0.624 -0.622 -0.62 ...
$ y        : num [1:512] 1.41e-06 8.22e-06 3.16e-05 7.85e-05 1.24e-04 ...
$ bw       : num 0.003
$ n        : int 1924150
$ call     : language density.default(x = all_noise)
$ data.name: chr "all_noise"
$ has.na   : logi FALSE
- attr(*, "class")= chr "density"

str(density(max_nearby))
List of 7
$ x        : num [1:512] 0.154 0.156 0.158 0.16 0.162 ...
$ y        : num [1:512] 0.00111 0.00125 0.0014 0.00157 0.00175 ...
$ bw       : num 0.0543
$ n        : int 250
$ call     : language density.default(x = max_nearby)
$ data.name: chr "max_nearby"
$ has.na   : logi FALSE
- attr(*, "class")= chr "density"

str(density(max_repeats ))
List of 7
$ x        : num [1:512] 0.272 0.274 0.275 0.277 0.279 ...
$ y        : num [1:512] 0.00507 0.00607 0.00722 0.00854 0.01011 ...
$ bw       : num 0.0261
$ n        : int 34
$ call     : language density.default(x = max_repeats)
$ data.name: chr "max_repeats"
$ has.na   : logi FALSE
- attr(*, "class")= chr "density"

Answer 1

The area under the density curves is 1, but they can exceed 1. I see nothing wrong with how you're doing this. For my own purposes about the only change I'd make would be to initialize the plot window with values so that all densities are in the bounds of the plot window.

Also, regarding the previous answer (I can't comment yet) notice that ylim is an argument to plot() , not to density() --- it's not telling density() to do anything.

Answer 2

kernel density plot is not a histogram. here is an example: take a look at the min and max of the density function and real min max of the data.

x <-rnorm(100)
min(x)
[1] -2.748188
max(x)
[1] 3.689254
density(x)
Call:
density.default(x = x)
Data: x (100 obs.); Bandwidth 'bw' = 0.4114

       x                 y            
 Min.   :-3.9823   Min.   :0.0001091  
 1st Qu.:-1.7559   1st Qu.:0.0079287  
 Median : 0.4705   Median :0.0612352  
 Mean   : 0.4705   Mean   :0.1121754  
 3rd Qu.: 2.6969   3rd Qu.:0.2267729  
 Max.   : 4.9234   Max.   :0.3439259 

plot(density(x))