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25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h5 class="title"> | |
27 | <a name="math_toolkit.stat_tut.weg.find_eg.find_location_eg"></a><a class="link" href="find_location_eg.html" title="Find Location (Mean) Example">Find | |
28 | Location (Mean) Example</a> | |
29 | </h5></div></div></div> | |
30 | <p> | |
31 | First we need some includes to access the normal distribution, the algorithms | |
32 | to find location (and some std output of course). | |
33 | </p> | |
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> | |
44 | ||
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> | |
51 | </pre> | |
52 | <p> | |
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. | |
56 | </p> | |
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> | |
59 | </pre> | |
60 | <p> | |
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). | |
64 | </p> | |
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> | |
67 | ||
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> | |
76 | </pre> | |
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 | |
79 | </pre> | |
80 | <p> | |
81 | We can now use ''find_location'' to give a new offset mean. | |
82 | </p> | |
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> | |
85 | </pre> | |
86 | <p> | |
87 | that outputs: | |
88 | </p> | |
89 | <pre class="programlisting">offset location (mean) = 1.09023 | |
90 | </pre> | |
91 | <p> | |
92 | showing that we need to shift the mean just over one standard deviation | |
93 | from its previous value of zero. | |
94 | </p> | |
95 | <p> | |
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): | |
98 | </p> | |
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> | |
100 | </pre> | |
101 | <p> | |
102 | And re-calculating the fraction below our chosen limit. | |
103 | </p> | |
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> | |
110 | </pre> | |
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 | |
113 | </pre> | |
114 | <h5> | |
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> | |
118 | </h5> | |
119 | <p> | |
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 | |
122 | ('bad' arguments). | |
123 | </p> | |
124 | <p> | |
125 | Unless we are using the boost::math namespace, we will need: | |
126 | </p> | |
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> | |
130 | </pre> | |
131 | <p> | |
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. | |
134 | </p> | |
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> | |
144 | </pre> | |
145 | <p> | |
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>. | |
149 | </p> | |
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> | |
153 | ||
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> | |
159 | </pre> | |
160 | <p> | |
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: | |
163 | </p> | |
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 | |
172 | </pre> | |
173 | </div> | |
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 Råde, 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>) | |
182 | </p> | |
183 | </div></td> | |
184 | </tr></table> | |
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188 | </div> | |
189 | </body> | |
190 | </html> |