<title>Normal (Gaussian) Distribution</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
-<link rel="home" href="../../../index.html" title="Math Toolkit 2.10.0">
+<link rel="home" href="../../../index.html" title="Math Toolkit 2.11.0">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_t_dist.html" title="Noncentral T Distribution">
<link rel="next" href="pareto.html" title="Pareto Distribution">
<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">normal_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">normal</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">normal_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
Normal Distribution</em></span>.
</p>
<p>
- Given mean μ  and standard deviation σ  it has the PDF:
- </p>
-<p>
-   <span class="inlinemediaobject"><img src="../../../../equations/normal_ref1.svg"></span>
+ Given mean μ and standard deviation σ it has the PDF:
</p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/normal_ref1.svg"></span>
+
+ </p></blockquote></div>
<p>
The variation the PDF with its parameters is illustrated in the following
graph:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/normal_pdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/normal_pdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
<p>
The cumulative distribution function is given by
</p>
-<p>
-   <span class="inlinemediaobject"><img src="../../../../equations/normal_cdf.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../equations/normal_cdf.svg"></span>
+
+ </p></blockquote></div>
<p>
and illustrated by this graph
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../../graphs/normal_cdf.svg" align="middle"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../../graphs/normal_cdf.svg" align="middle"></span>
+
+ </p></blockquote></div>
<h5>
<a name="math_toolkit.dist_ref.dists.normal_dist.h0"></a>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.normal_dist.member_functions"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist_ref.dists.normal_dist.member_functions">Member
standard deviation <span class="emphasis"><em>sd</em></span>.
</p>
<p>
- Requires sd > 0, otherwise <a class="link" href="../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
+ Requires <span class="emphasis"><em>sd</em></span> > 0, otherwise <a class="link" href="../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
is called.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="phrase"><a name="math_toolkit.dist_ref.dists.normal_dist.accuracy"></a></span><a class="link" href="normal_dist.html#math_toolkit.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
</h5>
<p>
- The normal distribution is implemented in terms of the <a class="link" href="../../sf_erf/error_function.html" title="Error Functions">error
+ The normal distribution is implemented in terms of the <a class="link" href="../../sf_erf/error_function.html" title="Error Function erf and complement erfc">error
function</a>, and as such should have very low error rates.
</p>
<h5>
</td>
<td>
<p>
- Using the relation: p = 0.5 * <a class="link" href="../../sf_erf/error_function.html" title="Error Functions">erfc</a>(-(x-m)/(s*sqrt(2)))
+ Using the relation: p = 0.5 * <a class="link" href="../../sf_erf/error_function.html" title="Error Function erf and complement erfc">erfc</a>(-(x-m)/(s*sqrt(2)))
</p>
</td>
</tr>
</td>
<td>
<p>
- Using the relation: q = 0.5 * <a class="link" href="../../sf_erf/error_function.html" title="Error Functions">erfc</a>((x-m)/(s*sqrt(2)))
+ Using the relation: q = 0.5 * <a class="link" href="../../sf_erf/error_function.html" title="Error Function erf and complement erfc">erfc</a>((x-m)/(s*sqrt(2)))
</p>
</td>
</tr>