<title>Uniform Distribution</title>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">uniform</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
- <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <a class="link" href="../../pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
+ <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a> <span class="special">=</span> <a class="link" href="../../pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy<></a> <span class="special">></span>
<span class="keyword">class</span> <span class="identifier">uniform_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">uniform_distribution</span><span class="special"><></span> <span class="identifier">uniform</span><span class="special">;</span>
- <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 19. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
+ <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
<span class="keyword">class</span> <span class="identifier">uniform_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
uniform distribution</a> is a distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
density function</a>:
</p>
-<p>
- f(x) =
- </p>
-<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
-<li class="listitem">
- 1 / (upper - lower) for lower < x < upper
- </li>
-<li class="listitem">
- zero for x < lower or x > upper
- </li>
-</ul></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">f(x) =1 / (upper - lower)   for lower <
+ x < upper</span>
+ </p></blockquote></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">f(x) =zero   for x < lower or x > upper</span>
+ </p></blockquote></div>
<p>
and in this implementation:
</p>
-<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
- 1 / (upper - lower) for x = lower or x = upper
- </li></ul></div>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="serif_italic">1 / (upper - lower)   for x = lower or x =
+ upper</span>
+ </p></blockquote></div>
<p>
- The choice of x = lower or x = upper is made because statistical use of
- this distribution judged is most likely: the method of maximum likelihood
- uses this definition.
+ The choice of <span class="emphasis"><em>x = lower</em></span> or <span class="emphasis"><em>x = upper</em></span>
+ is made because statistical use of this distribution judged is most likely:
+ the method of maximum likelihood uses this definition.
</p>
<p>
There is also a <a href="http://en.wikipedia.org/wiki/Discrete_uniform_distribution" target="_top"><span class="bold"><strong>discrete</strong></span> uniform distribution</a>.
</p>
<p>
The <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a>
- x must also be finite, and is supported lower <= x <= upper.
+ <span class="emphasis"><em>x</em></span> must also be finite, and is supported <span class="emphasis"><em>lower
+ <= x <= upper</em></span>.
</p>
<p>
The lower parameter is also called the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm" target="_top">location
The following graph illustrates how the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
density function PDF</a> varies with the shape parameter:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/uniform_pdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/uniform_pdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
Likewise for the CDF:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/uniform_cdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/uniform_cdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
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