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BenfordNarrow.gif (401 × 132 pixels, file size: 5 KB, MIME type: image/gif)

Summary

Description
English: A narrow probability distribution plotted on a log scale, to demonstrate a case where Benford's law does not hold. This is to be contrasted with BenfordBroad.gif.
Source Own work
Author Sbyrnes321
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Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
(* Source code written in Mathematica 6.0, by Steve Byrnes, 2008. I release this code into the public domain. *)

LabelsList = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 70, 100, 200, 300, 500, 1000, 2000, 5000, 10000};
LineList = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600,
   700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000};

gg[xx_] := Exp[-Abs[(xx - 60)/25]^1.8] xx

firstdig1[xx_] :=
  (1 < xx && xx < 2) || (10 < xx && xx < 20) || (100 < xx && xx < 200) || (1000 < xx && xx < 2000);
firstdig8[xx_] :=
  (8 < xx && xx < 9) || (80 < xx && xx < 90) || (800 < xx && xx < 900) || (8000 < xx && xx < 9000);

plotB = LogLinearPlot[{gg[x], If[firstdig1[x], gg[x], 0], If[firstdig8[x], gg[x], 0]}, {x, .995, 10100}, 
  Ticks -> {LabelsList, {}}, PlotRange -> All, TicksStyle -> Directive[Black, 10],
  GridLines -> {LineList, {}}, ImageSize -> 401, AspectRatio -> .3, 
  Filling -> {2 -> Bottom, 3 -> Bottom}, PlotPoints -> 1000, PlotStyle -> {Black, Red, Blue}, 
  FillingStyle -> {2 -> Red, 3 -> Blue}]

Export["plotB.gif", plotB, ImageSize -> 500]
 
This diagram was created with Mathematica by n.

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abf4327fdf76cf3d69af52ec4517cb3c9541811d

5,003 byte

132 pixel

401 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current21:46, 8 July 2009Thumbnail for version as of 21:46, 8 July 2009401 × 132 (5 KB)Sbyrnes321Changed scale to facilitate easier comparison with BenfordBroad.gif
04:47, 9 October 2008Thumbnail for version as of 04:47, 9 October 2008401 × 136 (3 KB)Sbyrnes321{{Information |Description={{en|1=A narrow probability distribution plotted on a log scale, to demonstrate a case where Benford's law does not hold. This is to be contrasted with BenfordBroad.gif.}} |Source=Own work by uploader |Author=[[User:Sbyrnes321|S

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