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26 <div class=
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27 <a name=
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28 Location (Mean) Example
</a>
29 </h5></div></div></div>
31 First we need some includes to access the normal distribution, the algorithms
32 to find location (and some std output of course).
34 <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">normal
</span><span class=
"special">.
</span><span class=
"identifier">hpp
</span><span class=
"special">></span> <span class=
"comment">// for normal_distribution
</span>
35 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">normal
</span><span class=
"special">;
</span> <span class=
"comment">// typedef provides default type is double.
</span>
36 <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">cauchy
</span><span class=
"special">.
</span><span class=
"identifier">hpp
</span><span class=
"special">></span> <span class=
"comment">// for cauchy_distribution
</span>
37 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">cauchy
</span><span class=
"special">;
</span> <span class=
"comment">// typedef provides default type is double.
</span>
38 <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">find_location
</span><span class=
"special">.
</span><span class=
"identifier">hpp
</span><span class=
"special">></span>
39 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">find_location
</span><span class=
"special">;
</span> <span class=
"comment">// for mean
</span>
40 <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">find_scale
</span><span class=
"special">.
</span><span class=
"identifier">hpp
</span><span class=
"special">></span>
41 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">find_scale
</span><span class=
"special">;
</span> <span class=
"comment">// for standard devation
</span>
42 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">complement
</span><span class=
"special">;
</span> <span class=
"comment">// Needed if you want to use the complement version.
</span>
43 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">policies
</span><span class=
"special">::
</span><span class=
"identifier">policy
</span><span class=
"special">;
</span>
45 <span class=
"preprocessor">#include
</span> <span class=
"special"><</span><span class=
"identifier">iostream
</span><span class=
"special">></span>
46 <span class=
"keyword">using
</span> <span class=
"identifier">std
</span><span class=
"special">::
</span><span class=
"identifier">cout
</span><span class=
"special">;
</span> <span class=
"keyword">using
</span> <span class=
"identifier">std
</span><span class=
"special">::
</span><span class=
"identifier">endl
</span><span class=
"special">;
</span>
47 <span class=
"preprocessor">#include
</span> <span class=
"special"><</span><span class=
"identifier">iomanip
</span><span class=
"special">></span>
48 <span class=
"keyword">using
</span> <span class=
"identifier">std
</span><span class=
"special">::
</span><span class=
"identifier">setw
</span><span class=
"special">;
</span> <span class=
"keyword">using
</span> <span class=
"identifier">std
</span><span class=
"special">::
</span><span class=
"identifier">setprecision
</span><span class=
"special">;
</span>
49 <span class=
"preprocessor">#include
</span> <span class=
"special"><</span><span class=
"identifier">limits
</span><span class=
"special">></span>
50 <span class=
"keyword">using
</span> <span class=
"identifier">std
</span><span class=
"special">::
</span><span class=
"identifier">numeric_limits
</span><span class=
"special">;
</span>
53 For this example, we will use the standard normal distribution, with
54 mean (location) zero and standard deviation (scale) unity. This is also
55 the default for this implementation.
57 <pre class=
"programlisting"><span class=
"identifier">normal
</span> <span class=
"identifier">N01
</span><span class=
"special">;
</span> <span class=
"comment">// Default 'standard' normal distribution with zero mean and
</span>
58 <span class=
"keyword">double
</span> <span class=
"identifier">sd
</span> <span class=
"special">=
</span> <span class=
"number">1.
</span><span class=
"special">;
</span> <span class=
"comment">// normal default standard deviation is
1.
</span>
61 Suppose we want to find a different normal distribution whose mean is
62 shifted so that only fraction p (here
0.001 or
0.1%) are below a certain
63 chosen limit (here -
2, two standard deviations).
65 <pre class=
"programlisting"><span class=
"keyword">double
</span> <span class=
"identifier">z
</span> <span class=
"special">=
</span> <span class=
"special">-
</span><span class=
"number">2.
</span><span class=
"special">;
</span> <span class=
"comment">// z to give prob p
</span>
66 <span class=
"keyword">double
</span> <span class=
"identifier">p
</span> <span class=
"special">=
</span> <span class=
"number">0.001</span><span class=
"special">;
</span> <span class=
"comment">// only
0.1% below z
</span>
68 <span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"Normal distribution with mean = "</span> <span class=
"special"><<</span> <span class=
"identifier">N01
</span><span class=
"special">.
</span><span class=
"identifier">location
</span><span class=
"special">()
</span>
69 <span class=
"special"><<</span> <span class=
"string">", standard deviation "</span> <span class=
"special"><<</span> <span class=
"identifier">N01
</span><span class=
"special">.
</span><span class=
"identifier">scale
</span><span class=
"special">()
</span>
70 <span class=
"special"><<</span> <span class=
"string">", has "</span> <span class=
"special"><<</span> <span class=
"string">"fraction <= "</span> <span class=
"special"><<</span> <span class=
"identifier">z
</span>
71 <span class=
"special"><<</span> <span class=
"string">", p = "</span> <span class=
"special"><<</span> <span class=
"identifier">cdf
</span><span class=
"special">(
</span><span class=
"identifier">N01
</span><span class=
"special">,
</span> <span class=
"identifier">z
</span><span class=
"special">)
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span>
72 <span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"Normal distribution with mean = "</span> <span class=
"special"><<</span> <span class=
"identifier">N01
</span><span class=
"special">.
</span><span class=
"identifier">location
</span><span class=
"special">()
</span>
73 <span class=
"special"><<</span> <span class=
"string">", standard deviation "</span> <span class=
"special"><<</span> <span class=
"identifier">N01
</span><span class=
"special">.
</span><span class=
"identifier">scale
</span><span class=
"special">()
</span>
74 <span class=
"special"><<</span> <span class=
"string">", has "</span> <span class=
"special"><<</span> <span class=
"string">"fraction > "</span> <span class=
"special"><<</span> <span class=
"identifier">z
</span>
75 <span class=
"special"><<</span> <span class=
"string">", p = "</span> <span class=
"special"><<</span> <span class=
"identifier">cdf
</span><span class=
"special">(
</span><span class=
"identifier">complement
</span><span class=
"special">(
</span><span class=
"identifier">N01
</span><span class=
"special">,
</span> <span class=
"identifier">z
</span><span class=
"special">))
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span> <span class=
"comment">// Note: uses complement.
</span>
77 <pre class=
"programlisting">Normal distribution with mean =
0, standard deviation
1, has fraction
<= -
2, p =
0.0227501
78 Normal distribution with mean =
0, standard deviation
1, has fraction
> -
2, p =
0.97725
81 We can now use ''find_location'' to give a new offset mean.
83 <pre class=
"programlisting"><span class=
"keyword">double
</span> <span class=
"identifier">l
</span> <span class=
"special">=
</span> <span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"identifier">p
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">);
</span>
84 <span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"offset location (mean) = "</span> <span class=
"special"><<</span> <span class=
"identifier">l
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span>
89 <pre class=
"programlisting">offset location (mean) =
1.09023
92 showing that we need to shift the mean just over one standard deviation
93 from its previous value of zero.
96 Then we can check that we have achieved our objective by constructing
97 a new distribution with the offset mean (but same standard deviation):
99 <pre class=
"programlisting"><span class=
"identifier">normal
</span> <span class=
"identifier">np001pc
</span><span class=
"special">(
</span><span class=
"identifier">l
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">);
</span> <span class=
"comment">// Same standard_deviation (scale) but with mean (location) shifted.
</span>
102 And re-calculating the fraction below our chosen limit.
104 <pre class=
"programlisting"><span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"Normal distribution with mean = "</span> <span class=
"special"><<</span> <span class=
"identifier">l
</span>
105 <span class=
"special"><<</span> <span class=
"string">" has "</span> <span class=
"special"><<</span> <span class=
"string">"fraction <= "</span> <span class=
"special"><<</span> <span class=
"identifier">z
</span>
106 <span class=
"special"><<</span> <span class=
"string">", p = "</span> <span class=
"special"><<</span> <span class=
"identifier">cdf
</span><span class=
"special">(
</span><span class=
"identifier">np001pc
</span><span class=
"special">,
</span> <span class=
"identifier">z
</span><span class=
"special">)
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span>
107 <span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"Normal distribution with mean = "</span> <span class=
"special"><<</span> <span class=
"identifier">l
</span>
108 <span class=
"special"><<</span> <span class=
"string">" has "</span> <span class=
"special"><<</span> <span class=
"string">"fraction > "</span> <span class=
"special"><<</span> <span class=
"identifier">z
</span>
109 <span class=
"special"><<</span> <span class=
"string">", p = "</span> <span class=
"special"><<</span> <span class=
"identifier">cdf
</span><span class=
"special">(
</span><span class=
"identifier">complement
</span><span class=
"special">(
</span><span class=
"identifier">np001pc
</span><span class=
"special">,
</span> <span class=
"identifier">z
</span><span class=
"special">))
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span>
111 <pre class=
"programlisting">Normal distribution with mean =
1.09023 has fraction
<= -
2, p =
0.001
112 Normal distribution with mean =
1.09023 has fraction
> -
2, p =
0.999
115 <a name=
"math_toolkit.stat_tut.weg.find_eg.find_location_eg.h0"></a>
116 <span class=
"phrase"><a name=
"math_toolkit.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_"></a></span><a class=
"link" href=
"find_location_eg.html#math_toolkit.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_">Controlling
117 Error Handling from find_location
</a>
120 We can also control the policy for handling various errors. For example,
121 we can define a new (possibly unwise) policy to ignore domain errors
125 Unless we are using the boost::math namespace, we will need:
127 <pre class=
"programlisting"><span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">policies
</span><span class=
"special">::
</span><span class=
"identifier">policy
</span><span class=
"special">;
</span>
128 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">policies
</span><span class=
"special">::
</span><span class=
"identifier">domain_error
</span><span class=
"special">;
</span>
129 <span class=
"keyword">using
</span> <span class=
"identifier">boost
</span><span class=
"special">::
</span><span class=
"identifier">math
</span><span class=
"special">::
</span><span class=
"identifier">policies
</span><span class=
"special">::
</span><span class=
"identifier">ignore_error
</span><span class=
"special">;
</span>
132 Using a typedef is often convenient, especially if it is re-used, although
133 it is not required, as the various examples below show.
135 <pre class=
"programlisting"><span class=
"keyword">typedef
</span> <span class=
"identifier">policy
</span><span class=
"special"><</span><span class=
"identifier">domain_error
</span><span class=
"special"><</span><span class=
"identifier">ignore_error
</span><span class=
"special">></span> <span class=
"special">></span> <span class=
"identifier">ignore_domain_policy
</span><span class=
"special">;
</span>
136 <span class=
"comment">// find_location with new policy, using typedef.
</span>
137 <span class=
"identifier">l
</span> <span class=
"special">=
</span> <span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"identifier">p
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">,
</span> <span class=
"identifier">ignore_domain_policy
</span><span class=
"special">());
</span>
138 <span class=
"comment">// Default policy policy
<>, needs
"using boost::math::policies::policy;"</span>
139 <span class=
"identifier">l
</span> <span class=
"special">=
</span> <span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"identifier">p
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">,
</span> <span class=
"identifier">policy
</span><span class=
"special"><>());
</span>
140 <span class=
"comment">// Default policy, fully specified.
</span>
141 <span class=
"identifier">l
</span> <span class=
"special">=
</span> <span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"identifier">p
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</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">policies
</span><span class=
"special">::
</span><span class=
"identifier">policy
</span><span class=
"special"><>());
</span>
142 <span class=
"comment">// A new policy, ignoring domain errors, without using a typedef.
</span>
143 <span class=
"identifier">l
</span> <span class=
"special">=
</span> <span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"identifier">p
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">,
</span> <span class=
"identifier">policy
</span><span class=
"special"><</span><span class=
"identifier">domain_error
</span><span class=
"special"><</span><span class=
"identifier">ignore_error
</span><span class=
"special">></span> <span class=
"special">>());
</span>
146 If we want to use a probability that is the
<a class=
"link" href=
"../../overview/complements.html" title=
"Complements are supported too - and when to use them">complements
</a>
147 of our probability, we should not even think of writing
<code class=
"computeroutput"><span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"number">1</span> <span class=
"special">-
</span> <span class=
"identifier">p
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">)
</span></code>, but use the complement version, see
148 <a class=
"link" href=
"../../overview/complements.html#why_complements">why complements?
</a>.
150 <pre class=
"programlisting"><span class=
"identifier">z
</span> <span class=
"special">=
</span> <span class=
"number">2.
</span><span class=
"special">;
</span>
151 <span class=
"keyword">double
</span> <span class=
"identifier">q
</span> <span class=
"special">=
</span> <span class=
"number">0.95</span><span class=
"special">;
</span> <span class=
"comment">// =
1 - p; // complement.
</span>
152 <span class=
"identifier">l
</span> <span class=
"special">=
</span> <span class=
"identifier">find_location
</span><span class=
"special"><</span><span class=
"identifier">normal
</span><span class=
"special">>(
</span><span class=
"identifier">complement
</span><span class=
"special">(
</span><span class=
"identifier">z
</span><span class=
"special">,
</span> <span class=
"identifier">q
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">));
</span>
154 <span class=
"identifier">normal
</span> <span class=
"identifier">np95pc
</span><span class=
"special">(
</span><span class=
"identifier">l
</span><span class=
"special">,
</span> <span class=
"identifier">sd
</span><span class=
"special">);
</span> <span class=
"comment">// Same standard_deviation (scale) but with mean(location) shifted
</span>
155 <span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"Normal distribution with mean = "</span> <span class=
"special"><<</span> <span class=
"identifier">l
</span> <span class=
"special"><<</span> <span class=
"string">" has "</span>
156 <span class=
"special"><<</span> <span class=
"string">"fraction <= "</span> <span class=
"special"><<</span> <span class=
"identifier">z
</span> <span class=
"special"><<</span> <span class=
"string">" = "</span> <span class=
"special"><<</span> <span class=
"identifier">cdf
</span><span class=
"special">(
</span><span class=
"identifier">np95pc
</span><span class=
"special">,
</span> <span class=
"identifier">z
</span><span class=
"special">)
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span>
157 <span class=
"identifier">cout
</span> <span class=
"special"><<</span> <span class=
"string">"Normal distribution with mean = "</span> <span class=
"special"><<</span> <span class=
"identifier">l
</span> <span class=
"special"><<</span> <span class=
"string">" has "</span>
158 <span class=
"special"><<</span> <span class=
"string">"fraction > "</span> <span class=
"special"><<</span> <span class=
"identifier">z
</span> <span class=
"special"><<</span> <span class=
"string">" = "</span> <span class=
"special"><<</span> <span class=
"identifier">cdf
</span><span class=
"special">(
</span><span class=
"identifier">complement
</span><span class=
"special">(
</span><span class=
"identifier">np95pc
</span><span class=
"special">,
</span> <span class=
"identifier">z
</span><span class=
"special">))
</span> <span class=
"special"><<</span> <span class=
"identifier">endl
</span><span class=
"special">;
</span>
161 See
<a href=
"../../../../../../example/find_location_example.cpp" target=
"_top">find_location_example.cpp
</a>
162 for full source code: the program output looks like this:
164 <pre class=
"programlisting">Example: Find location (mean).
165 Normal distribution with mean =
0, standard deviation
1, has fraction
<= -
2, p =
0.0227501
166 Normal distribution with mean =
0, standard deviation
1, has fraction
> -
2, p =
0.97725
167 offset location (mean) =
1.09023
168 Normal distribution with mean =
1.09023 has fraction
<= -
2, p =
0.001
169 Normal distribution with mean =
1.09023 has fraction
> -
2, p =
0.999
170 Normal distribution with mean =
0.355146 has fraction
<=
2 =
0.95
171 Normal distribution with mean =
0.355146 has fraction
> 2 =
0.05
174 <table xmlns:
rev=
"http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width=
"100%"><tr>
175 <td align=
"left"></td>
176 <td align=
"right"><div class=
"copyright-footer">Copyright
© 2006-
2010,
2012-
2014 Nikhar Agrawal,
177 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
178 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R
åde, Gautam Sewani,
179 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang
<p>
180 Distributed under the Boost Software License, Version
1.0. (See accompanying
181 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>)
186 <div class=
"spirit-nav">
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"p" href=
"../find_eg.html"><img src=
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"Prev"></a><a accesskey=
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