libs/math/doc/html/math_toolkit/stat_tut/overview/parameters.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Parameters can be calculated</title>
   5 <link rel="stylesheet" href="../../../math.css" type="text/css">
   6 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
   7 <link rel="home" href="../../../index.html" title="Math Toolkit 2.11.0">
   8 <link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
   9 <link rel="prev" href="complements.html" title="Complements are supported too - and when to use them">
  10 <link rel="next" href="summary.html" title="Summary">
  11 </head>
  12 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
  13 <table cellpadding="2" width="100%"><tr>
  14 <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
  15 <td align="center"><a href="../../../../../../../index.html">Home</a></td>
  16 <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
  17 <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
  18 <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
  19 <td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
  20 </tr></table>
  21 <hr>
  22 <div class="spirit-nav">
  23 <a accesskey="p" href="complements.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../overview.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="summary.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section">
  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="math_toolkit.stat_tut.overview.parameters"></a><a class="link" href="parameters.html" title="Parameters can be calculated">Parameters
  28         can be calculated</a>
  29 </h4></div></div></div>
  30 <p>
  31           Sometimes it's the parameters that define the distribution that you need
  32           to find. Suppose, for example, you have conducted a Students-t test for
  33           equal means and the result is borderline. Maybe your two samples differ
  34           from each other, or maybe they don't; based on the result of the test you
  35           can't be sure. A legitimate question to ask then is "How many more
  36           measurements would I have to take before I would get an X% probability
  37           that the difference is real?" Parameter finders can answer questions
  38           like this, and are necessarily different for each distribution. They are
  39           implemented as static member functions of the distributions, for example:
  40         </p>
  41 <pre class="programlisting"><span class="identifier">students_t</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
  42    <span class="number">1.3</span><span class="special">,</span>        <span class="comment">// difference from true mean to detect</span>
  43    <span class="number">0.05</span><span class="special">,</span>       <span class="comment">// maximum risk of falsely rejecting the null-hypothesis.</span>
  44    <span class="number">0.1</span><span class="special">,</span>        <span class="comment">// maximum risk of falsely failing to reject the null-hypothesis.</span>
  45    <span class="number">0.13</span><span class="special">);</span>      <span class="comment">// sample standard deviation</span>
  46 </pre>
  47 <p>
  48           Returns the number of degrees of freedom required to obtain a 95% probability
  49           that the observed differences in means is not down to chance alone. In
  50           the case that a borderline Students-t test result was previously obtained,
  51           this can be used to estimate how large the sample size would have to become
  52           before the observed difference was considered significant. It assumes,
  53           of course, that the sample mean and standard deviation are invariant with
  54           sample size.
  55         </p>
  56 </div>
  57 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
  58 <td align="left"></td>
  59 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
  60       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
  61       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
  62       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
  63       Daryle Walker and Xiaogang Zhang<p>
  64         Distributed under the Boost Software License, Version 1.0. (See accompanying
  65         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
  66       </p>
  67 </div></td>
  68 </tr></table>
  69 <hr>
  70 <div class="spirit-nav">
  71 <a accesskey="p" href="complements.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../overview.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="summary.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
  72 </div>
  73 </body>
  74 </html>