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BenfordBroad.png (500 × 165 pixels, file size: 3 KB, MIME type: image/png)

Summary

Description
English: A broad probability distribution on a log scale, with bars colored in to show why Benford's law holds
Source Own work
Author Sbyrnes321
This graph image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “BenfordBroad.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
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};

ff[x_] := 
  x Exp[-.1 x] .1 + x Exp[-.03 x] .03 +  x Exp[-.01 x] .01 + 
   x Exp[-.003 x] .003 + x Exp[-.001 x] .001 + x Exp[-.0003 x] .0003;

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);

plotA = LogLinearPlot[{ff[x], If[firstdig1[x], ff[x], 0], If[firstdig8[x], ff[x], 0]}, {x, .99, 10100}, 
  Ticks -> {LabelsList, {}}, PlotRange -> {0, 1}, 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["plotA.gif", plotA, ImageSize -> 500]

Original upload log

Date/Time Dimensions User Comment
9 October 2008, 04:44:33 500 × 165 (18087 bytes) Sbyrnes321 (talk · contribs) {{Information |Description={{en|1=A broad probability distribution on a log scale, with bars colored in to show why Benford's law holds}} |Source=Own work by uploader |Author=[[User:Sbyrnes321|Sbyrnes321]] |Date= |Permission= |other_versions= }} <!--{{Im

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30739a93beb8f8604bc0fa8e983084f58967ec48

3,471 byte

165 pixel

500 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current02:10, 24 August 2014Thumbnail for version as of 02:10, 24 August 2014500 × 165 (3 KB)GifTaggerBot: Converting file to superior PNG file. (Source: BenfordBroad.gif). This GIF was problematic due to non-greyscale color table.

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