nr02doc.htm

随机数生成程序

  <li>Indefinite</li>
  <li>Missing</li>
</ul>

<p>The arithmetic functions <tt>+</tt>, <tt>-</tt>, <tt>*</tt>, <tt>/</tt> are defined in
the obvious ways, as is <tt>&lt;&lt;</tt> for printing. The constructor can take either a
Real or a value of <tt>EXT_REAL_CODE</tt> as an argument. If there is no argument the
object is given the value <i>Missing</i>. Member function <tt>IsReal()</tt> returns <i>true</i>
if the enumeration value is <i>Finite</i> and in this case value of the Real can be found
with <tt>Value()</tt>. The enumeration value can be found with member function <tt>Code()</tt>.
</p>

<p><i>ExtReal</i> is used at the type for values returned from the <i>Mean</i> and <i>Variance</i>
member functions since these values may be infinite, indefinite or missing. </p>

<p>&nbsp; </p>

<h2><a NAME="supporting"></a><font COLOR="#FF0000">Descriptions of the supporting classes:</font></h2>

<h3><font COLOR="#FF0000">ChiSq1:</font></h3>

<p>Non-central chi-squared with one degree of freedom. Used as part of ChiSq. </p>

<h3><font COLOR="#FF0000">Gamma1:</font></h3>

<p>This generates random numbers from a gamma distribution with shape parameter <tt>alpha
&lt; 1</tt>. Because the density is infinite at <i>x</i> = 0 a power transform is
required. The constructor takes <tt>alpha</tt> as an argument. </p>

<h3><font COLOR="#FF0000">Gamma2:</font></h3>

<p>Gamma distribution for the shape parameter, <tt>alpha</tt>, greater than 1. The
constructor takes <tt>alpha</tt> as the argument. </p>

<h3><font COLOR="#FF0000">Poisson1:</font></h3>

<p>Poisson distribution; derived from AsymGen. The constructor takes the mean as the
argument. Used by Poisson for values of the mean greater than 10. </p>

<h3><font COLOR="#FF0000">Poisson2:</font></h3>

<p>Poisson distribution with mean less than or equal to 10. Uses DiscreteGen. Constructor
takes the mean as its argument. </p>

<h3><font COLOR="#FF0000">Binomial1:</font></h3>

<p>Binomial distribution; derived from AsymGen. Used by Binomial for <tt>n &gt;= 40</tt>.
Constructor takes <i>n</i> and <i>p</i> as arguments. </p>

<h3><font COLOR="#FF0000">Binomial2:</font></h3>

<p>Binomial distribution with <tt>n &lt; 40</tt>. Uses DiscreteGen. Constructor takes <i>n</i>
and <i>p</i> as arguments. </p>

<h3><font COLOR="#FF0000">AddedRandom, SubtractedRandom, MultipliedRandom, ShiftedRandom,
ReverseShiftedRandom, ScaledRandom, RepeatedRandom, SelectedRandom, AddedSelectedRandom:</font></h3>

<p>These are used by SumRandom and MixedRandom. </p>

<p>&nbsp; </p>

<h2><a NAME="generating"></a><font COLOR="#FF0000">Generating numbers from other
distributions:</font></h2>

<table BORDER="0" CELLSPACING="4" CELLPADDING="4">
  <tr>
    <th ALIGN="LEFT" VALIGN="TOP"><b>Distribution type</b></th>
    <th ALIGN="LEFT" VALIGN="TOP"><b>Method</b></th>
    <th ALIGN="LEFT" VALIGN="TOP"><b>Example</b></th>
  </tr>
  <tr>
    <td VALIGN="TOP">Continuous finite unimodal density (no parameters, can calculate density)</td>
    <td VALIGN="TOP">Use <a HREF="#posgenx">PosGenX</a>, <a HREF="#symgenx">SymGenX</a> or <a
    HREF="#asymgenx">AsymGenX</a>.</td>
    <td VALIGN="TOP"></td>
  </tr>
  <tr>
    <td VALIGN="TOP">Continuous finite unimodal density (with parameters, can calculate
    density)</td>
    <td VALIGN="TOP">Derive a new class from <a HREF="#posgen">PosGen</a>, <a HREF="#symgen">SymGen</a>
    or <a HREF="#asymgen">AsymGen</a>, over-ride <i>Density</i>.</td>
    <td VALIGN="TOP">Gamma2</td>
  </tr>
  <tr>
    <td VALIGN="TOP">Can calculate inverse of distribution</td>
    <td VALIGN="TOP">Transform <a HREF="#random">uniform random</a> number.</td>
    <td VALIGN="TOP">Pareto</td>
  </tr>
  <tr>
    <td VALIGN="TOP">Transformation of supported random number</td>
    <td VALIGN="TOP">Derive a new class from the existing class</td>
    <td VALIGN="TOP">ChiSq1</td>
  </tr>
  <tr>
    <td VALIGN="TOP">Transformation of several random numbers</td>
    <td VALIGN="TOP">Derive new class from <a HREF="#random">Random</a>; generate the new
    random number from the existing generators.</td>
    <td VALIGN="TOP">ChiSq</td>
  </tr>
  <tr>
    <td VALIGN="TOP">Density with infinite singularity</td>
    <td VALIGN="TOP">Transform a random variable generated by <a HREF="#posgen">PosGen</a>, <a
    HREF="#symgen">SymGen</a> or <a HREF="#asymgen">AsymGen</a>.</td>
    <td VALIGN="TOP">Gamma1</td>
  </tr>
  <tr>
    <td VALIGN="TOP">Distribution with several modes</td>
    <td VALIGN="TOP">Breakdown into a <a HREF="#mixed">mixture</a> of unimodal distributions.</td>
    <td VALIGN="TOP"></td>
  </tr>
  <tr>
    <td VALIGN="TOP">Linear or quadratic combination of supported random numbers</td>
    <td VALIGN="TOP">Use <a HREF="#sum">SumRandom</a>.</td>
    <td VALIGN="TOP"></td>
  </tr>
  <tr>
    <td VALIGN="TOP">Mixture of supported random numbers</td>
    <td VALIGN="TOP">Use <a HREF="#mixed">MixedRandom</a>.</td>
    <td VALIGN="TOP"></td>
  </tr>
  <tr>
    <td VALIGN="TOP">Discrete distribution (&lt; 100 possible values)</td>
    <td VALIGN="TOP">Use <a HREF="#discretegen">DiscreteGen</a>.</td>
    <td VALIGN="TOP">Poisson2</td>
  </tr>
  <tr>
    <td VALIGN="TOP">Discrete distribution (many possible values)</td>
    <td VALIGN="TOP">Use <a HREF="#posgen">PosGen</a>, <a HREF="#symgen">SymGen</a> or <a
    HREF="#asymgen">AsymGen</a>.</td>
    <td VALIGN="TOP">Poisson1</td>
  </tr>
</table>

<p>&nbsp; </p>

<h2><a NAME="other"></a><font COLOR="#FF0000">Other people's code:</font></h2>

<p>The gamma function and Shell sort routines are adapted from <i>Numerical Recipes in C</i>
by Press, Flannery, Teukolsky, Vetterling published by the Cambridge University Press. </p>

<p>&nbsp; </p>

<h2><a NAME="files"></a><font COLOR="#FF0000">Files included in this package:</font></h2>

<table BORDER="0" CELLSPACING="0" CELLPADDING="0" WIDTH="100%">
  <tr>
    <td VALIGN="TOP">readme.txt</td>
    <td VALIGN="TOP">readme file</td>
  </tr>
  <tr>
    <td VALIGN="TOP">newran.htm</td>
    <td VALIGN="TOP">this file</td>
  </tr>
  <tr>
    <td VALIGN="TOP">newran.h</td>
    <td VALIGN="TOP">header file for <i>newran</i></td>
  </tr>
  <tr>
    <td VALIGN="TOP">newran.cpp</td>
    <td VALIGN="TOP">main code file</td>
  </tr>
  <tr>
    <td VALIGN="TOP">extreal.h</td>
    <td VALIGN="TOP">header file for <i>extended reals</i></td>
  </tr>
  <tr>
    <td VALIGN="TOP">extreal.cpp</td>
    <td VALIGN="TOP">code file for <i>extended reals</i></td>
  </tr>
  <tr>
    <td VALIGN="TOP">boolean.h</td>
    <td VALIGN="TOP">definition of <i>bool</i></td>
  </tr>
  <tr>
    <td VALIGN="TOP">include.h</td>
    <td VALIGN="TOP">option file</td>
  </tr>
  <tr>
    <td VALIGN="TOP">tryrand.cpp</td>
    <td VALIGN="TOP">test file</td>
  </tr>
  <tr>
    <td VALIGN="TOP">tryrand1.cpp</td>
    <td VALIGN="TOP">called by tryrand - histograms of simple examples</td>
  </tr>
  <tr>
    <td VALIGN="TOP">tryrand2.cpp</td>
    <td VALIGN="TOP">called by tryrand - histograms of advanced examples</td>
  </tr>
  <tr>
    <td VALIGN="TOP">tryrand3.cpp</td>
    <td VALIGN="TOP">called by tryrand - statistical tests</td>
  </tr>
  <tr>
    <td VALIGN="TOP">tryrand4.cpp</td>
    <td VALIGN="TOP">called by tryrand - test permutations</td>
  </tr>
  <tr>
    <td VALIGN="TOP">hist.cpp</td>
    <td VALIGN="TOP">called by tryrand - draw histogram</td>
  </tr>
  <tr>
    <td VALIGN="TOP">tryrand.txt</td>
    <td VALIGN="TOP">output from tryrand</td>
  </tr>
  <tr>
    <td VALIGN="TOP">nrcc.mak</td>
    <td VALIGN="TOP">make file for CC compiler</td>
  </tr>
  <tr>
    <td VALIGN="TOP">nrgnu.mak</td>
    <td VALIGN="TOP">make file for gnu G++ compiler</td>
  </tr>
  <tr>
    <td VALIGN="TOP">nrwat.mak</td>
    <td VALIGN="TOP">makefile for Watcom 32 bit 10a compiler</td>
  </tr>
</table>

<p>&nbsp; </p>

<h2><a NAME="class"></a><font COLOR="#FF0000">Class structure:</font></h2>

<p>The following diagram gives the class hierarchy of the package. </p>

<pre><font SIZE="-1"><b>ExtReal</b>.......................... <i>Extended real numbers

</i><b>Random</b>........................... Uniform random number generator
&nbsp;|
&nbsp;+---Constant.................... Return a constant
&nbsp;|
&nbsp;+---PosGen...................... Used by PosGenX etc
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---PosGenX................ Positive random #s from decreasing density
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---Exponential............ Negative exponential rng
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---Gamma1................. Used by Gamma (shape parameter &lt; 1)
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---SymGen................. Used by SymGenX etc
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; +---SymGenX........... Random numbers from symmetric density
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; +---Cauchy............ Cauchy random number generator
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; +---Normal............ Standard normal random number generator
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; +---ChiSq1....... Used by ChiSq (one df)
&nbsp;|&nbsp;
&nbsp;+---AsymGen..................... Used by AsymGenX etc
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---AsymGenX............... Random numbers from asymmetric density
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---Poisson1............... Used by Poisson (mean &gt; 8)
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---Binomial1.............. Used by Binomial (n &gt;= 40)
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---NegativeBinomial....... Negative binomial random number generator
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---Gamma2................. Used by Gamma (shape parameter &gt; 1)
&nbsp;|
&nbsp;+---ChiSq....................... Non-central chi-squared rng
&nbsp;|
&nbsp;+---Gamma....................... Gamma random number generator
&nbsp;|
&nbsp;+---Pareto...................... Pareto random number generator
&nbsp;|
&nbsp;+---DiscreteGen................. Discrete random number generator
&nbsp;|
&nbsp;+---Poisson2.................... Used by Poisson (mean &lt;= 8)
&nbsp;|
&nbsp;+---Binomial2................... Used by Binomial (n &lt; 40)
&nbsp;|
&nbsp;+---Poisson..................... Poisson random number generator
&nbsp;|
&nbsp;+---Binomial.................... Binomial random number generator
&nbsp;|
&nbsp;+---SumRandom................... Sum of random numbers
&nbsp;|
&nbsp;+---MixedRandom................. Mixture of random numbers
&nbsp;|
&nbsp;+---MultipliedRandom............ Used by SumRandom
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---AddedRandom............ Used by SumRandom
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---SubtractedRandom....... Used by SumRandom
&nbsp;|
&nbsp;+---ShiftedRandom............... Used by SumRandom
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---ReverseShiftedRandom... Used by SumRandom
&nbsp;|&nbsp;&nbsp;&nbsp; |
&nbsp;|&nbsp;&nbsp;&nbsp; +---ScaledRandom........... Used by SumRandom
&nbsp;|
&nbsp;+---NegatedRandom.......... .... Used by SumRandom
&nbsp;|
&nbsp;+---RepeatedRandom.............. Used by SumRandom
&nbsp;|
&nbsp;+---AddedSelectedRandom......... Used by MixedRandom
&nbsp;|
&nbsp;+---SelectedRandom.............. Used by MixedRandom

<b>RandomPermutation</b>................ Random permutation
&nbsp;|
&nbsp;+---RandomCombination........... Sorted random permutation</font></pre>

<p>&nbsp; </p>

<h2><a NAME="todo"></a><font COLOR="#FF0000">To do:</font></h2>

<ul>
  <li>More modern alternatives to the <a HREF="#random">LGM generator</a>;</li>
  <li>Additional generator classes;</li>
  <li>Better methods for combinations and permutations with large <tt>N</tt> and small <tt>M</tt>;</li>
  <li>An alternative (slower) class for Poisson with short setup time.</li>
</ul>

<p>&nbsp;</p>

<h2><a name="history"></a><font COLOR="#FF0000">History:</font></h2>

<p>August, 1998 - update exception package; work around problem with MS VC++ 5</p>

<p>January, 1998 - version compatible with newmat09</p>

<p>1995 - <em>newran</em> version, additional distributions</p>

<p>1989 - initial version</p>

<hr>

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<p><a HREF="ol_doc.htm">To online documentation page</a>&nbsp; </p>
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