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Below is the source input I used for this validation:

  1. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
  4. <head><meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
  5. <meta name="Author" lang="en" content="Miguel Casquilho" />
  7. <title>M&middot;C, IST: sum of 2 Gaussians</title>
  10. <link rel="stylesheet" type="text/css"
  11. href="http://web.tecnico.ulisboa.pt/~mcasquilho/common/x_commonstyle.css" />
  12. <style type="text/css">
  13. body {background-image: url("http://web.tecnico.ulisboa.pt/~mcasquilho/common/circles-green.jpeg") } </style>
  14. <style type="text/css">
  15. a.special:hover {color: inherit; background-color: aqua} </style>
  16. </head> <!-- 26Apr2019 Apr2017 12Sep2009 MC -->
  18. <body class="sm">
  19. <form method="post" action=
  20. "http://web.tecnico.ulisboa.pt/~mcasquilho/cgi-bin/transfer.php?Sum2Gauss">
  21. <input name="executable" type="hidden" value="Sum2Gauss.exe" />
  23. <table width="90%" bgcolor="#eeeeee" align="center" border="1">
  24. <tr><td colspan="3">
  25. <table width="100%"> <!--title-->
  26. <tr><td width="50px"><a href='https://fenix.ist.utl.pt/departamentos/deq'><img alt='&copy;'
  27. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/MC.gif" border='0'
  28. width='40' height='41' /></a>
  29. </td>
  30. <td><div style="font-size: 13.5pt; text-align: center"><!-- title --><b
  31. onmouseout="this.style.color='blue', this.style.fontStyle='normal'"
  32. onmouseover="this.style.color='red',
  33. this.style.fontStyle='bold'">
  34. Sum of
  35. two Gaussians</b></div><center>Draws Monte Carlo simulated curves
  36. for 2 Gaussians
  37. and their sum.<!--b> UNDER&nbsp;CONSTRUCTION</b--></center></td>
  38. <td width="112px"><table width='100%'>
  39. <tr><td align='center' bgcolor='white'>
  40. <input type="submit"
  41. value="&nbsp; Execute &nbsp;" style="background-color: #00bfff"
  42. onmouseout="this.style.fontStyle='normal', this.style.fontWeight='normal'"
  43. onmouseover="this.style.fontStyle='normal', this.style.fontWeight='bold'" /></td>
  44. </tr><tr><td align='center'><span style='font-size:
  45. xx-small'>2021.Mar.16 03:49:47</span></td></tr>
  46. </table>
  47. </td></tr></table>
  48. </td></tr> <!-- ................................................... -->
  50. <tr><td width="15%" align="center"><i>&mu;</i><sub>1</sub>,
  51. <i>&sigma;</i><sub>1</sub></td>
  52. <td width="45%"><input name="zmu1" type="text" value="9" size="4"
  53. maxlength="6" /><input name="sig1" type="text" value=".3" size="4"
  54. maxlength="6" /></td>
  55. <td>Parameters of the 1.st variable.</td></tr>
  57. <tr><td align="center"><i>&mu;</i><sub>2</sub>,
  58. <i>&sigma;</i><sub>2</sub></td>
  59. <td><input name="zmu2" type="text" value="5" size="4"
  60. maxlength="6" /><input name="sig2" type="text" value=".4" size="4"
  61. maxlength="6" /></td>
  62. <td>Parameters of the 2.nd variable.</td></tr>
  64. <tr><td align="center">ntr, .repeat, klass</td>
  65. <td>10^<input name="zntrlg" type="text" value="5.30" size="4"
  66. maxlength="4" />; <input name="irepeat" type="text" value="0" size="6"
  67. maxlength="10" /><select name="klass"><option value="100">100</option>
  68. <option value="200" selected="selected">200</option></select></td>
  69. <td>N. of trials, repeatability, n.&nbsp;of&nbsp;histogram
  70. classes. &bull;</td></tr>
  72. <tr><td align="center">Show values ?</td>
  73. <td><select name="ishow"><option value="0" selected="selected">No</option>
  74. <option value="1">Yes</option></select></td>
  75. <td>Shows the values of the graph coordinates.</td></tr>
  77. <!-- plot gnudata.dat \ (or anything: this line is a MANDATORY dummy) -->
  79. <tr><td colspan="3"><input name="gnuplot" type="hidden"
  80. value="wid = 600.
  81. set terminal png enhanced font 'Times, 16' size wid, wid/1.618
  82. set title 'Sum of 2 Gaussians' offset 0, -0.8
  83. set timestamp font 'Helvetica-Bold, 9' offset +5, +0.75
  84. set key top right font ', 12'
  85. set xlabel '{/Times-Italic x}' offset wid/50., +0.6
  86. #set lmargin at screen 25; set rmargin 5 # not working ?
  87. set lmargin 5; set rmargin 5
  88. set ylabel ' {/Times-Italic f}({/Times-Italic x})' rotate by 0 \
  89. offset 1.5, +3 # +2.75, 0
  90. set yrange [0:*]
  91. set tics font ', 13'
  92. #set lmargin at screen 25; set rmargin 5 # not working ?
  94. set grid xtics y2tics; set lmargin 7; set rmargin 6
  95. set style data filledcurves y1=0
  96. set style fill transparent solid 0.1 # border with filledcurves y1=0
  98. set style line 11 lc rgb 'red' lw 3
  99. set style line 12 lc rgb '#09ad00' lw 3 # green
  100. set style line 13 lc -1 lw 2
  101. set style line 14 lc rgb 'blue' lw 1 # '#0000ff' blue # '#ff1010' ?
  103. plot anyname.dat \
  104. usi 1:2 title '{/Times-Italic x}_1' with lines ls 11, \
  105. '' usi 1:3 title '{/Times-Italic x}_2' with lines ls 12, \
  106. '' usi 1:4 title '{/Times-Italic x}_S' with lines ls 13
  107. EOD
  108. " />&emsp;
  109. Draws 3 "Monte Carlo" <i>simulated</i> curves:
  110. for the 2 Gaussian variables (summands),
  111. <i>X</i><sub>1</sub> and <i>X</i><sub>2</sub>;
  112. and for the sum, <i>X</i> = <i>X</i><sub>1</sub> + <i>X</i><sub>2</sub>.
  113. It can be <i>verified</i> (as stated theoretically) that
  114. &nbsp;<i>(a)</i> the sum also is Gaussian, &nbsp;<i>(b)</i> with parameters:
  115. <i>&mu;</i> = <i>&mu;</i><sub>1</sub> + <i>&mu;</i><sub>2</sub> and
  116. <i>&sigma;</i> = &radic;(<i>&sigma;</i><sub>1</sub>&sup2; +
  117. <i>&sigma;</i><sub>2</sub>&sup2;) &nbsp;(from
  118. <i>&sigma;</i>&sup2;&nbsp;=
  119. <i>&sigma;</i><sub>1</sub>&sup2;&nbsp;+&nbsp;<i>&sigma;</i><sub>2</sub>&sup2;).
  120. <br />&emsp;Other suggested data sets (<i>&mu;, &sigma;</i>):
  121. 34, 0.33 / 66, 0.56;&emsp;
  122. 10, 1 / 11, 1;&emsp;
  123. 10, 0.5 / 10, 1.2;&emsp;
  124. 10, 3 / 20, 4 .
  125. <br />&emsp;[Pythagorean triples: (3, 4, 5), (5, 12, 13), (7, 24, 25),
  126. (8, 15, 17)...]</td></tr>
  128. <tr><td align="center"><input type="reset" style="font-size: smaller"
  129. value=" Reset " /></td><td><i>References:</i></td>
  130. <td align="center">Plate: Sum2Gaussians</td></tr>
  131. <tr><td colspan="3"><p class="ref">&bull;&nbsp;<span
  132. class="sc">Weisstein</span>, "<a href=
  133. "http://mathworld.wolfram.com/NormalSumDistribution.html"
  134. >Normal sum distribution</a>". From <i>MathWorld</i>&mdash;a
  135. Wolfram web resource.</p>
  137. <p class="ref">&bull;&nbsp;B. <a href=
  138. "http://web.ist.utl.pt/ist162478/PPIII/example.php">Franco</a> or
  139. <a href=
  140. "http://web.ist.utl.pt/ist11038/compute/qc/new/example.php">here</a>
  141. &bull;&nbsp;Search <a href=
  142. "http://www.google.pt/search?hl=en&amp;q=%22Monte+Carlo%22+method"><i>Monte
  143. Carlo</i> method</a>...</p>
  145. <p class="ref">&bull;&nbsp;<a href=
  146. "http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
  147. (Wikipedia) &bull;&nbsp;"<a href=
  148. "http://www.cs.princeton.edu/introcs/11gaussian/">Gaussian or Normal</a>
  149. distribution ?" (Dept. of Computer Sci., Princeton U.).</p>
  151. <p class="ref">&bull;&nbsp;<span class="sc">Gorard</span>, Stephen, 2004,
  152. <a href="http://www.leeds.ac.uk/educol/documents/00003759.htm">Revisiting
  153. a 90-year-old debate: the advantages of the mean deviation</a>, <i>British
  154. Educational Research Association Annual Conference,</i> 16&ndash;18 Sep.
  155. (Univ. of York).</p>
  157. <p class="ref">&bull;&nbsp;<span
  158. class="sc">Weisstein</span>, "<a href=
  159. "http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean triple</a>".
  160. From <i>MathWorld</i>&mdash;a Wolfram web resource.</p>
  162. <p class="ref">&bull;&nbsp;1873-09-13: <a href=
  163. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Caratheodory.html"
  164. ><span class="sc">Carathéodory</span></a>, Constantin
  165. (1950-02-02).</p></td></tr>
  166. </table>
  167. </form>
  169. <div style="line-height: 12pt">&nbsp;</div>
  170. <div style="line-height: 1.5pt; color: black;
  171. background-color: red">&nbsp;</div>
  173. <table width="100%" class="sm"><tr>
  174. <td style="width: 58px"><a href=
  175. "http://validator.w3.org/check?uri=http://web.tecnico.ulisboa.pt/~mcasquilho/compute/qc/Fx-sum-2Gauss.php;verbose=1;ss=1"><img
  176. src="http://web.tecnico.ulisboa.pt/~mcasquilho/common/valid-xhtml10s.png"
  177. alt="Valid HTML 4.01!" style="border: none"
  178. width="55px" height="19px" /></a></td>
  179. <td style="width: 15%" align="left"><a href=
  180. "http://www.tecnico.ulisboa.pt"><img
  181. src="http://web.tecnico.ulisboa.pt/~mcasquilho/common/wwwist.png" alt="IST"
  182. style="vertical-align: middle; border: none;
  183. width: 88px; height: 34px" /></a></td>
  184. <td style="width: 70%" align="right"><i>http://web.tecnico.ulisboa.pt/~mcasquilho/compute/qc/Fx-sum-2Gauss.php</i><br />
  185. <i>Created:</i> 2009-09-13 &mdash; <i>Last modified:</i>
  186. 2019-04-28</td></tr></table>
  187. </body></html>

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