File:WrappedNormalPDF.png
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Summary
| Description |
English: PDF of the wrapped normal distribution. |
| Date | |
| Source | Own work |
| Author | PAR |
Created using the following Mathematica program:
$Assumptions = s > 0
f[x_, m_, s_] = Exp[-(x - m)^2/(2*s^2)]/(s*Sqrt[2*Pi])
fw[][Theta]_, m_, s_] =
Sum[][][Theta] + 2*Pi*n, m, s], {n, -Infinity,
Infinity}] (* Wrapped normal distribution for angle \[Theta] *)
p1 = Plot[][][Theta]*Pi, 0, Sqrt[1/8], {\[Theta], -1, 1},
PlotStyle -> {Magenta, Thick}];
p2 = Plot[][][Theta]*Pi, 0, Sqrt[1/4], {\[Theta], -1, 1},
PlotStyle -> {Red, Thick}];
p3 = Plot[][][Theta]*Pi, 0, Sqrt[1/2], {\[Theta], -1, 1},
PlotStyle -> {Green, Thick}];
p4 = Plot[][][Theta]*Pi, 0, Sqrt[1/1], {\[Theta], -1, 1},
PlotStyle -> {Cyan, Thick}];
p5 = Plot[][][Theta]*Pi, 0, Sqrt[2 ], {\[Theta], -1, 1},
PlotStyle -> {Blue, Thick}];
p6 = Plot[][Theta], -1, 1}, PlotStyle -> {Black, Thick}];
Show[{p1, p2, p3, p4, p5, p6}, PlotRange -> {{-1, 1}, {0, 1}},
Frame -> True]
p1 = Plot[][][][Theta]p*Pi, 0,
Sqrt[1/8], {\[Theta]p, -1, \[Theta]}], {\[Theta], -1, 1},
PlotStyle -> {Magenta, Thick}];
p2 = Plot[][][][Theta]p*Pi, 0,
Sqrt[1/4], {\[Theta]p, -1, \[Theta]}], {\[Theta], -1, 1},
PlotStyle -> {Red, Thick}];
p3 = Plot[][][][Theta]p*Pi, 0,
Sqrt[1/2], {\[Theta]p, -1, \[Theta]}], {\[Theta], -1, 1},
PlotStyle -> {Green, Thick}];
p4 = Plot[][][][Theta]p*Pi, 0,
Sqrt[1/1], {\[Theta]p, -1, \[Theta]}], {\[Theta], -1, 1},
PlotStyle -> {Cyan, Thick}];
p5 = Plot[][][][Theta]p*Pi, 0,
Sqrt[2/1], {\[Theta]p, -1, \[Theta]}], {\[Theta], -1, 1},
PlotStyle -> {Blue, Thick}];
p0 = Plot[][][Theta]p, -1, \ \[Theta]}], {\[Theta], -1, 1}, PlotStyle -> {Black, Thick}];
Show[{p0, p1, p2, p3, p4, p5}, PlotRange -> {{-1, 1}, {0, 1}},
Frame -> True]
Licensing
 
|
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.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 05:17, 23 May 2011 | | 1,435 × 947 (68 KB) | wikimediacommons>PAR~commonswiki | {{Information |Description ={{en|1=PDF of the wrapped normal distribution. }} |Source ={{own}} |Author =PAR |Date =2011-05-22 |Permission = |other_versions = }} Created using the following Mathematica program: |
