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26 <div class=
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27 <a name=
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28 </h4></div></div></div>
29 <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>
30 <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>
31 <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>
32 <span class=
"keyword">class
</span> <a class=
"link" href=
"../../../policy.html" title=
"Chapter 15. 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>
33 <span class=
"keyword">class
</span> <span class=
"identifier">uniform_distribution
</span><span class=
"special">;
</span>
35 <span class=
"keyword">typedef
</span> <span class=
"identifier">uniform_distribution
</span><span class=
"special"><></span> <span class=
"identifier">uniform
</span><span class=
"special">;
</span>
37 <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 15. Policies: Controlling Precision, Error Handling etc">Policy
</a><span class=
"special">></span>
38 <span class=
"keyword">class
</span> <span class=
"identifier">uniform_distribution
</span>
39 <span class=
"special">{
</span>
40 <span class=
"keyword">public
</span><span class=
"special">:
</span>
41 <span class=
"keyword">typedef
</span> <span class=
"identifier">RealType
</span> <span class=
"identifier">value_type
</span><span class=
"special">;
</span>
43 <span class=
"identifier">uniform_distribution
</span><span class=
"special">(
</span><span class=
"identifier">RealType
</span> <span class=
"identifier">lower
</span> <span class=
"special">=
</span> <span class=
"number">0</span><span class=
"special">,
</span> <span class=
"identifier">RealType
</span> <span class=
"identifier">upper
</span> <span class=
"special">=
</span> <span class=
"number">1</span><span class=
"special">);
</span> <span class=
"comment">// Constructor.
</span>
44 <span class=
"special">:
</span> <span class=
"identifier">m_lower
</span><span class=
"special">(
</span><span class=
"identifier">lower
</span><span class=
"special">),
</span> <span class=
"identifier">m_upper
</span><span class=
"special">(
</span><span class=
"identifier">upper
</span><span class=
"special">)
</span> <span class=
"comment">// Default is standard uniform distribution.
</span>
45 <span class=
"comment">// Accessor functions.
</span>
46 <span class=
"identifier">RealType
</span> <span class=
"identifier">lower
</span><span class=
"special">()
</span><span class=
"keyword">const
</span><span class=
"special">;
</span>
47 <span class=
"identifier">RealType
</span> <span class=
"identifier">upper
</span><span class=
"special">()
</span><span class=
"keyword">const
</span><span class=
"special">;
</span>
48 <span class=
"special">};
</span> <span class=
"comment">// class uniform_distribution
</span>
50 <span class=
"special">}}
</span> <span class=
"comment">// namespaces
</span>
53 The uniform distribution, also known as a rectangular distribution, is
54 a probability distribution that has constant probability.
57 The
<a href=
"http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target=
"_top">continuous
58 uniform distribution
</a> is a distribution with the
<a href=
"http://en.wikipedia.org/wiki/Probability_density_function" target=
"_top">probability
64 <div class=
"itemizedlist"><ul class=
"itemizedlist" style=
"list-style-type: disc; ">
66 1 / (upper - lower) for lower
< x
< upper
69 zero for x
< lower or x
> upper
73 and in this implementation:
75 <div class=
"itemizedlist"><ul class=
"itemizedlist" style=
"list-style-type: disc; "><li class=
"listitem">
76 1 / (upper - lower) for x = lower or x = upper
79 The choice of x = lower or x = upper is made because statistical use of
80 this distribution judged is most likely: the method of maximum likelihood
84 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>.
87 Parameters lower and upper can be any finite value.
90 The
<a href=
"http://en.wikipedia.org/wiki/Random_variate" target=
"_top">random variate
</a>
91 x must also be finite, and is supported lower
<= x
<= upper.
94 The lower parameter is also called the
<a href=
"http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm" target=
"_top">location
95 parameter
</a>,
<a href=
"http://en.wikipedia.org/wiki/Location_parameter" target=
"_top">that
96 is where the origin of a plot will lie
</a>, and (upper - lower) is
97 also called the
<a href=
"http://en.wikipedia.org/wiki/Scale_parameter" target=
"_top">scale
101 The following graph illustrates how the
<a href=
"http://en.wikipedia.org/wiki/Probability_density_function" target=
"_top">probability
102 density function PDF
</a> varies with the shape parameter:
105 <span class=
"inlinemediaobject"><img src=
"../../../../graphs/uniform_pdf.svg" align=
"middle"></span>
108 Likewise for the CDF:
111 <span class=
"inlinemediaobject"><img src=
"../../../../graphs/uniform_cdf.svg" align=
"middle"></span>
114 <a name=
"math_toolkit.dist_ref.dists.uniform_dist.h0"></a>
115 <span class=
"phrase"><a name=
"math_toolkit.dist_ref.dists.uniform_dist.member_functions"></a></span><a class=
"link" href=
"uniform_dist.html#math_toolkit.dist_ref.dists.uniform_dist.member_functions">Member
118 <pre class=
"programlisting"><span class=
"identifier">uniform_distribution
</span><span class=
"special">(
</span><span class=
"identifier">RealType
</span> <span class=
"identifier">lower
</span> <span class=
"special">=
</span> <span class=
"number">0</span><span class=
"special">,
</span> <span class=
"identifier">RealType
</span> <span class=
"identifier">upper
</span> <span class=
"special">=
</span> <span class=
"number">1</span><span class=
"special">);
</span>
121 Constructs a
<a href=
"http://en.wikipedia.org/wiki/uniform_distribution" target=
"_top">uniform
122 distribution
</a> with lower
<span class=
"emphasis"><em>lower
</em></span> (a) and upper
123 <span class=
"emphasis"><em>upper
</em></span> (b).
126 Requires that the
<span class=
"emphasis"><em>lower
</em></span> and
<span class=
"emphasis"><em>upper
</em></span>
127 parameters are both finite; otherwise if infinity or NaN then calls
<a class=
"link" href=
"../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error
</a>.
129 <pre class=
"programlisting"><span class=
"identifier">RealType
</span> <span class=
"identifier">lower
</span><span class=
"special">()
</span><span class=
"keyword">const
</span><span class=
"special">;
</span>
132 Returns the
<span class=
"emphasis"><em>lower
</em></span> parameter of this distribution.
134 <pre class=
"programlisting"><span class=
"identifier">RealType
</span> <span class=
"identifier">upper
</span><span class=
"special">()
</span><span class=
"keyword">const
</span><span class=
"special">;
</span>
137 Returns the
<span class=
"emphasis"><em>upper
</em></span> parameter of this distribution.
140 <a name=
"math_toolkit.dist_ref.dists.uniform_dist.h1"></a>
141 <span class=
"phrase"><a name=
"math_toolkit.dist_ref.dists.uniform_dist.non_member_accessors"></a></span><a class=
"link" href=
"uniform_dist.html#math_toolkit.dist_ref.dists.uniform_dist.non_member_accessors">Non-member
145 All the
<a class=
"link" href=
"../nmp.html" title=
"Non-Member Properties">usual non-member accessor
146 functions
</a> that are generic to all distributions are supported:
147 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.cdf">Cumulative Distribution Function
</a>,
148 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.pdf">Probability Density Function
</a>,
149 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.quantile">Quantile
</a>,
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.hazard">Hazard Function
</a>,
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.chf">Cumulative Hazard Function
</a>,
150 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.mean">mean
</a>,
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.median">median
</a>,
151 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.mode">mode
</a>,
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.variance">variance
</a>,
152 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.sd">standard deviation
</a>,
153 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.skewness">skewness
</a>,
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.kurtosis">kurtosis
</a>,
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.kurtosis_excess">kurtosis_excess
</a>,
154 <a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.range">range
</a> and
<a class=
"link" href=
"../nmp.html#math_toolkit.dist_ref.nmp.support">support
</a>.
157 The domain of the random variable is any finite value, but the supported
158 range is only
<span class=
"emphasis"><em>lower
</em></span> <= x
<=
<span class=
"emphasis"><em>upper
</em></span>.
161 <a name=
"math_toolkit.dist_ref.dists.uniform_dist.h2"></a>
162 <span class=
"phrase"><a name=
"math_toolkit.dist_ref.dists.uniform_dist.accuracy"></a></span><a class=
"link" href=
"uniform_dist.html#math_toolkit.dist_ref.dists.uniform_dist.accuracy">Accuracy
</a>
165 The uniform distribution is implemented with simple arithmetic operators
166 and so should have errors within an epsilon or two.
169 <a name=
"math_toolkit.dist_ref.dists.uniform_dist.h3"></a>
170 <span class=
"phrase"><a name=
"math_toolkit.dist_ref.dists.uniform_dist.implementation"></a></span><a class=
"link" href=
"uniform_dist.html#math_toolkit.dist_ref.dists.uniform_dist.implementation">Implementation
</a>
173 In the following table a is the
<span class=
"emphasis"><em>lower
</em></span> parameter of
174 the distribution, b is the
<span class=
"emphasis"><em>upper
</em></span> parameter,
<span class=
"emphasis"><em>x
</em></span>
175 is the random variate,
<span class=
"emphasis"><em>p
</em></span> is the probability and
<span class=
"emphasis"><em>q
178 <div class=
"informaltable"><table class=
"table">
204 Using the relation: pdf =
0 for x
< a,
1 / (b - a) for a
<=
205 x
<= b,
0 for x
> b
217 Using the relation: cdf =
0 for x
< a, (x - a) / (b - a) for
218 a
<= x
<= b,
1 for x
> b
230 Using the relation: q =
1 - p, (b - x) / (b - a)
242 Using the relation: x = p * (b - a) + a;
249 quantile from the complement
278 (b - a)
<sup>2</sup> /
12
290 any value in [a, b] but a is chosen. (Would NaN be better?)
314 -
6/
5 = -
1.2 exactly. (kurtosis -
3)
333 <a name=
"math_toolkit.dist_ref.dists.uniform_dist.h4"></a>
334 <span class=
"phrase"><a name=
"math_toolkit.dist_ref.dists.uniform_dist.references"></a></span><a class=
"link" href=
"uniform_dist.html#math_toolkit.dist_ref.dists.uniform_dist.references">References
</a>
336 <div class=
"itemizedlist"><ul class=
"itemizedlist" style=
"list-style-type: disc; ">
337 <li class=
"listitem">
338 <a href=
"http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target=
"_top">Wikpedia
339 continuous uniform distribution
</a>
341 <li class=
"listitem">
342 <a href=
"http://mathworld.wolfram.com/UniformDistribution.html" target=
"_top">Weisstein,
343 Weisstein, Eric W.
"Uniform Distribution." From MathWorld--A
344 Wolfram Web Resource.
</a>
346 <li class=
"listitem">
347 <a href=
"http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm" target=
"_top">http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm
</a>
351 <table xmlns:
rev=
"http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width=
"100%"><tr>
352 <td align=
"left"></td>
353 <td align=
"right"><div class=
"copyright-footer">Copyright
© 2006-
2010,
2012-
2014 Nikhar Agrawal,
354 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
355 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R
åde, Gautam Sewani,
356 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang
<p>
357 Distributed under the Boost Software License, Version
1.0. (See accompanying
358 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>)
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