File:Standard symmetric pdfs.svg

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Summary

Description
English: Plot of several symmetric unimodal probability densities with unit variance. From highest to lowest peak:
 
red, kurtosis 3, Laplace (D)ouble exponential distribution;
 
orange, kurtosis 2, hyperbolic (S)ecant distribution;
 
green, kurtosis 1.2, (L)ogistic distribution;
 
black, kurtosis 0, (N)ormal distribution;
 
cyan, kurtosis −0.593762…, raised (C)osine distribution;
 
blue, kurtosis −1, (W)igner semicircle distribution;
 
magenta, kurtosis −1.2, (U)niform distribution.
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Public domain This chart is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. For more information, see Commons:Threshold of originality § Charts

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Other versions File:Standard symmetric pdfs logscale.svg
File:Standard symmetric pdfs.png
File:Standard symmetric pdfs logscale.png
SVG development
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 The SVG code is valid.
 This chart was created with Gnuplot.
Source code
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Gnuplot code

# Laplace double exponential distribution, kurtosis 3
laplace(x) = exp(-abs(x)*sqrt(2)) * sqrt(0.5)

# sech distribution, kurtosis 2
sech(x) = 2.0 / (exp(x) + exp(-x))
sech_pdf(x) = 0.5 * sech(0.5*pi*x)

# logistic distribution, kurtosis 1.2
slogist = sqrt(3) / pi
logist(x) = exp(-x/slogist) / slogist / (1 + exp(-x/slogist))**2

# normal distribution, kurtosis 0
n(x) = exp(-0.5*x*x) / sqrt(2*pi)

# raised cosine distribution, kurtosis -0.59376
scos = 1.0 / sqrt(1/3.0 - 2/pi**2)
cosine(x) = abs(x)>scos? 0 : (1+cos(x*pi/scos))*0.5/scos

# Wigner semicircle distribution, kurtosis -1
wigner(x) = abs(x)>2? 0 : sqrt(4-x*x)*0.5/pi

# uniform distribution, kurtosis -1.2
uniform(x) = abs(x)>sqrt(3)? 0 : 0.5/sqrt(3)

set samples 6001
set grid

set xrange [-5.4:5.4]
set xtics 1

set key right font ",8" enhanced

set terminal svg size 400,300 enhanced fname 'DejaVu Sans'  fsize 10 butt solid
set output 'Standard symmetric pdfs.svg'

plot \
     laplace(x)  lt 1 lw 2 title "D,  3", \
     sech_pdf(x) lt 8 lw 2 title "S,  2", \
     logist(x)   lt 2 lw 2 title "L,  1.2", \
     n(x)        lt 7 lw 2 title "N,  0", \
     cosine(x)   lt 5 lw 2 title "C, -0.59376", \
     wigner(x)   lt 3 lw 2 title "W, -1", \
     uniform(x)  lt 4 lw 2 title "U, -1.2"

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26 May 2020

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Date/TimeThumbnailDimensionsUserComment
current17:15, 26 May 2020Thumbnail for version as of 17:15, 26 May 2020400 × 300 (390 KB)wikimediacommons>Andelsmall legend tweak

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