
BoostCommit : 
Subject: [Boostcommit] svn:boost r50075  sandbox/math_toolkit/libs/math/example
From: pbristow_at_[hidden]
Date: 20081202 12:16:04
Author: pbristow
Date: 20081202 12:16:03 EST (Tue, 02 Dec 2008)
New Revision: 50075
URL: http://svn.boost.org/trac/boost/changeset/50075
Log:
A very noddy example for Laplace distribution. Better ideas?
Added:
sandbox/math_toolkit/libs/math/example/laplace_example.cpp (contents, props changed)
Added: sandbox/math_toolkit/libs/math/example/laplace_example.cpp
==============================================================================
 (empty file)
+++ sandbox/math_toolkit/libs/math/example/laplace_example.cpp 20081202 12:16:03 EST (Tue, 02 Dec 2008)
@@ 0,0 +1,171 @@
+// laplace_example.cpp
+
+// Copyright Paul A. Bristow 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+// Example of using laplace (& comparing with normal) distribution.
+
+// Note that this file contains Quickbook markup as well as code
+// and comments, don't change any of the special comment markups!
+
+//[laplace_example1
+/*`
+First we need some includes to access the laplace & normal distributions
+(and some std output of course).
+*/
+
+#include <boost/math/distributions/laplace.hpp> // for laplace_distribution
+ using boost::math::laplace; // typedef provides default type is double.
+#include <boost/math/distributions/normal.hpp> // for normal_distribution
+ using boost::math::normal; // typedef provides default type is double.
+
+#include <iostream>
+ using std::cout; using std::endl; using std::left; using std::showpoint; using std::noshowpoint;
+#include <iomanip>
+ using std::setw; using std::setprecision;
+#include <limits>
+ using std::numeric_limits;
+
+int main()
+{
+ cout << "Example: Laplace distribution." << endl;
+
+ try
+ {
+ { // Traditional tables and values.
+/*`Let's start by printing some traditional tables.
+*/
+ double step = 1.; // in z
+ double range = 4; // min and max z = range to +range.
+ //int precision = 17; // traditional tables are only computed to much lower precision.
+ int precision = 4; // traditional table at much lower precision.
+ int width = 10; // for use with setw.
+
+ // Construct standard laplace & normal distributions l & s
+ normal s; // (default location or mean = zero, and scale or standard deviation = unity)
+ cout << "Standard normal distribution, mean or location = "<< s.location()
+ << ", standard deviation or scale = " << s.scale() << endl;
+ laplace l; // (default mean = zero, and standard deviation = unity)
+ cout << "Laplace normal distribution, location = "<< l.location()
+ << ", scale = " << l.scale() << endl;
+
+/*` First the probability distribution function (pdf).
+*/
+ cout << "Probability distribution function values" << endl;
+ cout << " z PDF normal laplace (difference)" << endl;
+ cout.precision(5);
+ for (double z = range; z < range + step; z += step)
+ {
+ cout << left << setprecision(3) << setw(6) << z << " "
+ << setprecision(precision) << setw(width) << pdf(s, z) << " "
+ << setprecision(precision) << setw(width) << pdf(l, z)<< " ("
+ << setprecision(precision) << setw(width) << pdf(l, z)  pdf(s, z) // difference.
+ << ")" << endl;
+ }
+ cout.precision(6); // default
+/*`Notice how the laplace is less at z = 1 , but has 'fatter' tails at 2 and 3.
+
+ And the area under the normal curve from [infin] up to z,
+ the cumulative distribution function (cdf).
+*/
+ // For a standard distribution
+ cout << "Standard location = "<< s.location()
+ << ", scale = " << s.scale() << endl;
+ cout << "Integral (area under the curve) from  infinity up to z " << endl;
+ cout << " z CDF normal laplace (difference)" << endl;
+ for (double z = range; z < range + step; z += step)
+ {
+ cout << left << setprecision(3) << setw(6) << z << " "
+ << setprecision(precision) << setw(width) << cdf(s, z) << " "
+ << setprecision(precision) << setw(width) << cdf(l, z) << " ("
+ << setprecision(precision) << setw(width) << cdf(l, z)  cdf(s, z) // difference.
+ << ")" << endl;
+ }
+ cout.precision(6); // default
+
+/*`
+Prettyprinting a traditional 2dimensional table is left as an exercise for the student,
+but why bother now that the Boost Math Toolkit lets you write
+*/
+ double z = 2.;
+ cout << "Area for gaussian z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.
+ cout << "Area for laplace z = " << z << " is " << cdf(l, z) << endl; //
+/*`
+Correspondingly, we can obtain the traditional 'critical' values for significance levels.
+For the 95% confidence level, the significance level usually called alpha,
+is 0.05 = 1  0.95 (for a onesided test), so we can write
+*/
+ cout << "95% of gaussian area has a z below " << quantile(s, 0.95) << endl;
+ cout << "95% of laplace area has a z below " << quantile(l, 0.95) << endl;
+ // 95% of area has a z below 1.64485
+ // 95% of laplace area has a z below 2.30259
+/*`and a twosided test (a comparison between two levels, rather than a onesided test)
+
+*/
+ cout << "95% of gaussian area has a z between " << quantile(s, 0.975)
+ << " and " << quantile(s, 0.975) << endl;
+ cout << "95% of laplace area has a z between " << quantile(l, 0.975)
+ << " and " << quantile(l, 0.975) << endl;
+ // 95% of area has a z between 1.95996 and 1.95996
+ // 95% of laplace area has a z between 2.99573 and 2.99573
+/*`Notice how much wider z has to be to enclose 95% of the area.
+*/
+ }
+//] [/[laplace_example1]
+ }
+ catch(const std::exception& e)
+ { // Always useful to include try & catch blocks because default policies
+ // are to throw exceptions on arguments that cause errors like underflow, overflow.
+ // Lacking try & catch blocks, the program will abort without a message below,
+ // which may give some helpful clues as to the cause of the exception.
+ std::cout <<
+ "\n""Message from thrown exception was:\n " << e.what() << std::endl;
+ }
+ return 0;
+} // int main()
+
+
+/*
+
+Output is:
+
+Example: Laplace distribution.
+Standard normal distribution, mean or location = 0, standard deviation or scale = 1
+Laplace normal distribution, location = 0, scale = 1
+Probability distribution function values
+ z PDF normal laplace (difference)
+4 0.0001338 0.009158 (0.009024 )
+3 0.004432 0.02489 (0.02046 )
+2 0.05399 0.06767 (0.01368 )
+1 0.242 0.1839 (0.05803 )
+0 0.3989 0.5 (0.1011 )
+1 0.242 0.1839 (0.05803 )
+2 0.05399 0.06767 (0.01368 )
+3 0.004432 0.02489 (0.02046 )
+4 0.0001338 0.009158 (0.009024 )
+Standard location = 0, scale = 1
+Integral (area under the curve) from  infinity up to z
+ z CDF normal laplace (difference)
+4 3.167e005 0.009158 (0.009126 )
+3 0.00135 0.02489 (0.02354 )
+2 0.02275 0.06767 (0.04492 )
+1 0.1587 0.1839 (0.02528 )
+0 0.5 0.5 (0 )
+1 0.8413 0.8161 (0.02528 )
+2 0.9772 0.9323 (0.04492 )
+3 0.9987 0.9751 (0.02354 )
+4 1 0.9908 (0.009126 )
+Area for gaussian z = 2 is 0.97725
+Area for laplace z = 2 is 0.932332
+95% of gaussian area has a z below 1.64485
+95% of laplace area has a z below 2.30259
+95% of gaussian area has a z between 1.95996 and 1.95996
+95% of laplace area has a z between 2.99573 and 2.99573
+
+
+*/
+
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