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diff --git a/src/boost/libs/math/example/laplace_example.cpp b/src/boost/libs/math/example/laplace_example.cpp new file mode 100644 index 00000000..ed99dba2 --- /dev/null +++ b/src/boost/libs/math/example/laplace_example.cpp @@ -0,0 +1,169 @@ +// laplace_example.cpp + +// Copyright Paul A. Bristow 2008, 2010. + +// 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 mark-up as well as code +// and comments, don't change any of the special comment mark-ups! + +//[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 + +/*` +Pretty-printing a traditional 2-dimensional 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 one-sided 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 two-sided test (a comparison between two levels, rather than a one-sided 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 3.167e-005 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 + +*/ + |