| // find_location.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 finding location (mean) |
| // for normal (Gaussian) & Cauchy 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! |
| |
| //#ifdef _MSC_VER |
| //# pragma warning(disable: 4180) // qualifier has no effect (in Fusion). |
| //#endif |
| |
| //[find_location1 |
| /*` |
| First we need some includes to access the normal distribution, |
| the algorithms to find location (and some std output of course). |
| */ |
| |
| #include <boost/math/distributions/normal.hpp> // for normal_distribution |
| using boost::math::normal; // typedef provides default type is double. |
| #include <boost/math/distributions/cauchy.hpp> // for cauchy_distribution |
| using boost::math::cauchy; // typedef provides default type is double. |
| #include <boost/math/distributions/find_location.hpp> |
| using boost::math::find_location; // for mean |
| #include <boost/math/distributions/find_scale.hpp> |
| using boost::math::find_scale; // for standard devation |
| using boost::math::complement; // Needed if you want to use the complement version. |
| using boost::math::policies::policy; |
| |
| #include <iostream> |
| using std::cout; using std::endl; |
| #include <iomanip> |
| using std::setw; using std::setprecision; |
| #include <limits> |
| using std::numeric_limits; |
| |
| //] [/find_location1] |
| |
| int main() |
| { |
| cout << "Example: Find location (or mean)." << endl; |
| try |
| { |
| //[find_location2 |
| /*` |
| For this example, we will use the standard normal distribution, |
| with mean (location) zero and standard deviation (scale) unity. |
| This is also the default for this implementation. |
| */ |
| normal N01; // Default 'standard' normal distribution with zero mean and |
| double sd = 1.; // normal default standard deviation is 1. |
| /*`Suppose we want to find a different normal distribution whose mean is shifted |
| so that only fraction p (here 0.001 or 0.1%) are below a certain chosen limit |
| (here -2, two standard deviations). |
| */ |
| double z = -2.; // z to give prob p |
| double p = 0.001; // only 0.1% below z |
| |
| cout << "Normal distribution with mean = " << N01.location() |
| << ", standard deviation " << N01.scale() |
| << ", has " << "fraction <= " << z |
| << ", p = " << cdf(N01, z) << endl; |
| cout << "Normal distribution with mean = " << N01.location() |
| << ", standard deviation " << N01.scale() |
| << ", has " << "fraction > " << z |
| << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. |
| /*` |
| [pre |
| Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501 |
| Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p = 0.97725 |
| ] |
| We can now use ''find_location'' to give a new offset mean. |
| */ |
| double l = find_location<normal>(z, p, sd); |
| cout << "offset location (mean) = " << l << endl; |
| /*` |
| that outputs: |
| [pre |
| offset location (mean) = 1.09023 |
| ] |
| showing that we need to shift the mean just over one standard deviation from its previous value of zero. |
| |
| Then we can check that we have achieved our objective |
| by constructing a new distribution |
| with the offset mean (but same standard deviation): |
| */ |
| normal np001pc(l, sd); // Same standard_deviation (scale) but with mean (location) shifted. |
| /*` |
| And re-calculating the fraction below our chosen limit. |
| */ |
| cout << "Normal distribution with mean = " << l |
| << " has " << "fraction <= " << z |
| << ", p = " << cdf(np001pc, z) << endl; |
| cout << "Normal distribution with mean = " << l |
| << " has " << "fraction > " << z |
| << ", p = " << cdf(complement(np001pc, z)) << endl; |
| /*` |
| [pre |
| Normal distribution with mean = 1.09023 has fraction <= -2, p = 0.001 |
| Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999 |
| ] |
| |
| [h4 Controlling Error Handling from find_location] |
| We can also control the policy for handling various errors. |
| For example, we can define a new (possibly unwise) |
| policy to ignore domain errors ('bad' arguments). |
| |
| Unless we are using the boost::math namespace, we will need: |
| */ |
| using boost::math::policies::policy; |
| using boost::math::policies::domain_error; |
| using boost::math::policies::ignore_error; |
| |
| /*` |
| Using a typedef is often convenient, especially if it is re-used, |
| although it is not required, as the various examples below show. |
| */ |
| typedef policy<domain_error<ignore_error> > ignore_domain_policy; |
| // find_location with new policy, using typedef. |
| l = find_location<normal>(z, p, sd, ignore_domain_policy()); |
| // Default policy policy<>, needs "using boost::math::policies::policy;" |
| l = find_location<normal>(z, p, sd, policy<>()); |
| // Default policy, fully specified. |
| l = find_location<normal>(z, p, sd, boost::math::policies::policy<>()); |
| // A new policy, ignoring domain errors, without using a typedef. |
| l = find_location<normal>(z, p, sd, policy<domain_error<ignore_error> >()); |
| /*` |
| If we want to use a probability that is the |
| [link complements complement of our probability], |
| we should not even think of writing `find_location<normal>(z, 1 - p, sd)`, |
| but, [link why_complements to avoid loss of accuracy], use the complement version. |
| */ |
| z = 2.; |
| double q = 0.95; // = 1 - p; // complement. |
| l = find_location<normal>(complement(z, q, sd)); |
| |
| normal np95pc(l, sd); // Same standard_deviation (scale) but with mean(location) shifted |
| cout << "Normal distribution with mean = " << l << " has " |
| << "fraction <= " << z << " = " << cdf(np95pc, z) << endl; |
| cout << "Normal distribution with mean = " << l << " has " |
| << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl; |
| //] [/find_location2] |
| } |
| 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() |
| |
| //[find_location_example_output |
| /*` |
| [pre |
| Example: Find location (mean). |
| Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501 |
| Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p = 0.97725 |
| offset location (mean) = 1.09023 |
| Normal distribution with mean = 1.09023 has fraction <= -2, p = 0.001 |
| Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999 |
| Normal distribution with mean = 0.355146 has fraction <= 2 = 0.95 |
| Normal distribution with mean = 0.355146 has fraction > 2 = 0.05 |
| ] |
| */ |
| //] [/find_location_example_output] |