Etydhv

I am trying to draw a histogram next to a density function, both with data from a file. The histogram is already working:

documentclass[tikz,border=3.14mm]standalone
usepackagepgfplots

beginfilecontentsexample.dat
71
54
55
54
98
76
93
95
86
88
68
68
50
61
79
79
73
57
56
57
97
80
91
94
85
88
45
58
78
81
74
60
57
58
95
81
endfilecontents

begindocument
 begintikzpicture
 beginaxis[ybar, ymin=0]

 addplot[fill=black,
 hist=
 bins=11
 ] table [y index=0] example.dat;

 endaxis
 endtikzpicture

enddocument

My question is with the density function.
I would like to draw it using this formular (kernel density estimation):

EDIT start

where:

• n: Number of datapoints




• sigma: Standard deviation (User input)




• x_i: Datapoint i




• x: Function input variable (f(x))

EDIT end

I can't just plot it using addplot... because f(x) depends on all datapoints x_i.

I was thinking about using something like that somewhere:

pgfplotstablereadexample.dattable
pgfplotstablegetrowsoftable
pgfmathsetmacroRpgfplotsretval-1

pgfplotsinvokeforeach0,...,R
 pgfplotstablegetelem#10oftable
 pgfmathsetmacro value pgfplotsretval
 % sum up all e^0.5(value-x)/sigma somhow

But I couldn't find a way to define a variable where I can add values in every iteration.

Here is an image from Wikipedia on Kernel density estimation:

The blue curve on the right is kind of what I would like to draw.
What's the best way of achieving that?

You can sum these things up as follow. I use pgfplotsforeachungrouped in order to avoid making the variables global. I used some prescription to generate something. If you make your prescription more explicit, this can be adjusted accordingly.

documentclass[tikz,border=3.14mm]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
beginfilecontents*example.dat
71
54
55
54
98
76
93
95
86
88
68
68
50
61
79
79
73
57
56
57
97
80
91
94
85
88
45
58
78
81
74
60
57
58
95
81
endfilecontents*

begindocument
 begintikzpicture
pgfplotstablereadexample.datdatatable
pgfplotstablegetrowsofdatatable
pgfmathsetmacroRpgfplotsretval-1
pgfmathsetmacromysum0
pgfplotsforeachungrouped X in 0,...,R
 pgfplotstablegetelemX0ofdatatable
 edefmysummysum+2*exp(-(x-pgfplotsretval-0.5)^2)
 % sum up all e^0.5(value-x)/sigma somhow


 beginaxis[ ymin=0]

 addplot[ybar,fill=black,
 hist=
 bins=11
 ] table [y index=0] example.dat;
 addplot[blue,domain=40:100,thick,samples=501] mysum;
 endaxis
 endtikzpicture

enddocument

If you use

edefmysummysum+sqrt(2)*exp(-0.25*(x-pgfplotsretval-0.5)^2)

instead, you get

OLD ANSWER: I am not sure I got the normalization of the Gaussian right.

documentclass[tikz,border=3.14mm]standalone
usepackagepgfplots
pgfplotssetcompat=1.16
beginfilecontents*example.dat
71
54
55
54
98
76
93
95
86
88
68
68
50
61
79
79
73
57
56
57
97
80
91
94
85
88
45
58
78
81
74
60
57
58
95
81
endfilecontents*

begindocument
 begintikzpicture
pgfplotstablereadexample.datdatatable
pgfplotstablegetrowsofdatatable
pgfmathsetmacroRpgfplotsretval-1
pgfmathsetmacromysum0
pgfplotsforeachungrouped X in 0,...,R
 pgfplotstablegetelemX0ofdatatable
 pgfmathsetmacromysummysum+pgfplotsretval
 % sum up all e^0.5(value-x)/sigma somhow

pgfmathsetmacromyaveragemysum/R
pgfmathsetmacromysigma0
pgfplotsforeachungrouped X in 0,...,R
 pgfplotstablegetelemX0ofdatatable
 pgfmathsetmacromysigmamysigma+pow(pgfplotsretval-myaverage,2)


%typeoutmysum,myaverage,mysigma

 beginaxis[ ymin=0]

 addplot[ybar,fill=black,
 hist=
 bins=11
 ] table [y index=0] example.dat;
 addplot[blue,domain=0:100,thick,samples=101] sqrt(4*mysigma/(R*R))*exp(-R*(x-myaverage)^2/mysigma);
 endaxis
 endtikzpicture

enddocument

documentclassarticle
beginfilecontentsexample.dat
71
54
.
.
.
95
81
endfilecontents
begindocument
<<echo=F,fig.cap="Histogram and density plot.">>=
data <- read.csv("example.dat", comment.char = "%",header=F)
hist(data$V1, freq=F, col="gray", main="", xlab="Example data")
lines(density(data$V1),col="blue",lwd=3)
@
enddocument

Of course, you can have some control over the density function, for instance with:

lines(density(data$V1,adjust=.5, bw=8),col="blue",lwd=3)

The result will be ...