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553 lines
24 KiB
C++
553 lines
24 KiB
C++
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// test_fisher_squared.cpp
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// Copyright Paul A. Bristow 2006.
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// Copyright John Maddock 2007.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/tools/test.hpp>
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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using ::boost::math::concepts::real_concept;
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#include <boost/math/distributions/fisher_f.hpp> // for fisher_f_distribution
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using boost::math::fisher_f_distribution;
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // for test_main
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#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
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#include "test_out_of_range.hpp"
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#include <iostream>
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using std::cout;
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using std::endl;
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#include <limits>
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using std::numeric_limits;
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template <class RealType>
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RealType naive_pdf(RealType df1, RealType df2, RealType x)
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{
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//
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// Calculate the PDF naively using direct evaluation
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// of equation 2 from http://mathworld.wolfram.com/F-Distribution.html
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//
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// Our actual PDF implementation uses a completely different method,
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// so this is a good sanity check that our math is correct.
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//
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using namespace std; // For ADL of std functions.
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RealType e = boost::math::lgamma((df1 + df2) / 2);
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e += log(df1) * df1 / 2;
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e += log(df2) * df2 / 2;
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e += log(x) * ((df1 / 2) - 1);
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e -= boost::math::lgamma(df1 / 2);
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e -= boost::math::lgamma(df2 / 2);
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e -= log(df2 + x * df1) * (df1 + df2) / 2;
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return exp(e);
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}
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template <class RealType>
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void test_spot(
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RealType df1, // Degrees of freedom 1
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RealType df2, // Degrees of freedom 2
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RealType cs, // Chi Square statistic
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RealType P, // CDF
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RealType Q, // Complement of CDF
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RealType tol) // Test tolerance
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{
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boost::math::fisher_f_distribution<RealType> dist(df1, df2);
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BOOST_CHECK_CLOSE(
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cdf(dist, cs), P, tol);
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BOOST_CHECK_CLOSE(
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pdf(dist, cs), naive_pdf(dist.degrees_of_freedom1(), dist.degrees_of_freedom2(), cs), tol);
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if((P < 0.999) && (Q < 0.999))
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{
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//
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// We can only check this if P is not too close to 1,
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// so that we can guarantee Q is free of error:
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//
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BOOST_CHECK_CLOSE(
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cdf(complement(dist, cs)), Q, tol);
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BOOST_CHECK_CLOSE(
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quantile(dist, P), cs, tol);
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BOOST_CHECK_CLOSE(
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quantile(complement(dist, Q)), cs, tol);
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}
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}
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//
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// This test data is taken from the tables of upper
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// critical values of the F distribution available
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// at http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm
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//
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double q[] = { 0.10, 0.05, 0.025, 0.01, 0.001 };
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double upper_critical_values[][10] = {
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{ 161.448,199.500,215.707,224.583,230.162,233.986,236.768,238.882,240.543,241.882 },
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{ 18.513, 19.000, 19.164, 19.247, 19.296, 19.330, 19.353, 19.371, 19.385, 19.396 },
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{ 10.128, 9.552, 9.277, 9.117, 9.013, 8.941, 8.887, 8.845, 8.812, 8.786 },
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{ 7.709, 6.944, 6.591, 6.388, 6.256, 6.163, 6.094, 6.041, 5.999, 5.964 },
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{ 6.608, 5.786, 5.409, 5.192, 5.050, 4.950, 4.876, 4.818, 4.772, 4.735 },
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{ 5.987, 5.143, 4.757, 4.534, 4.387, 4.284, 4.207, 4.147, 4.099, 4.060 },
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{ 5.591, 4.737, 4.347, 4.120, 3.972, 3.866, 3.787, 3.726, 3.677, 3.637 },
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{ 5.318, 4.459, 4.066, 3.838, 3.687, 3.581, 3.500, 3.438, 3.388, 3.347 },
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{ 5.117, 4.256, 3.863, 3.633, 3.482, 3.374, 3.293, 3.230, 3.179, 3.137 },
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{ 4.965, 4.103, 3.708, 3.478, 3.326, 3.217, 3.135, 3.072, 3.020, 2.978 },
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{ 4.844, 3.982, 3.587, 3.357, 3.204, 3.095, 3.012, 2.948, 2.896, 2.854 },
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{ 4.747, 3.885, 3.490, 3.259, 3.106, 2.996, 2.913, 2.849, 2.796, 2.753 },
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{ 4.667, 3.806, 3.411, 3.179, 3.025, 2.915, 2.832, 2.767, 2.714, 2.671 },
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{ 4.600, 3.739, 3.344, 3.112, 2.958, 2.848, 2.764, 2.699, 2.646, 2.602 },
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{ 4.543, 3.682, 3.287, 3.056, 2.901, 2.790, 2.707, 2.641, 2.588, 2.544 },
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{ 4.494, 3.634, 3.239, 3.007, 2.852, 2.741, 2.657, 2.591, 2.538, 2.494 },
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{ 4.451, 3.592, 3.197, 2.965, 2.810, 2.699, 2.614, 2.548, 2.494, 2.450 },
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{ 4.414, 3.555, 3.160, 2.928, 2.773, 2.661, 2.577, 2.510, 2.456, 2.412 },
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{ 4.381, 3.522, 3.127, 2.895, 2.740, 2.628, 2.544, 2.477, 2.423, 2.378 },
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{ 4.351, 3.493, 3.098, 2.866, 2.711, 2.599, 2.514, 2.447, 2.393, 2.348 },
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{ 4.325, 3.467, 3.072, 2.840, 2.685, 2.573, 2.488, 2.420, 2.366, 2.321 },
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{ 4.301, 3.443, 3.049, 2.817, 2.661, 2.549, 2.464, 2.397, 2.342, 2.297 },
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{ 4.279, 3.422, 3.028, 2.796, 2.640, 2.528, 2.442, 2.375, 2.320, 2.275 },
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{ 4.260, 3.403, 3.009, 2.776, 2.621, 2.508, 2.423, 2.355, 2.300, 2.255 },
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{ 4.242, 3.385, 2.991, 2.759, 2.603, 2.490, 2.405, 2.337, 2.282, 2.236 },
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{ 4.225, 3.369, 2.975, 2.743, 2.587, 2.474, 2.388, 2.321, 2.265, 2.220 },
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{ 4.210, 3.354, 2.960, 2.728, 2.572, 2.459, 2.373, 2.305, 2.250, 2.204 },
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{ 4.196, 3.340, 2.947, 2.714, 2.558, 2.445, 2.359, 2.291, 2.236, 2.190 },
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{ 4.183, 3.328, 2.934, 2.701, 2.545, 2.432, 2.346, 2.278, 2.223, 2.177 },
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{ 4.171, 3.316, 2.922, 2.690, 2.534, 2.421, 2.334, 2.266, 2.211, 2.165 },
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{ 4.160, 3.305, 2.911, 2.679, 2.523, 2.409, 2.323, 2.255, 2.199, 2.153 },
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{ 4.149, 3.295, 2.901, 2.668, 2.512, 2.399, 2.313, 2.244, 2.189, 2.142 },
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{ 4.139, 3.285, 2.892, 2.659, 2.503, 2.389, 2.303, 2.235, 2.179, 2.133 },
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{ 4.130, 3.276, 2.883, 2.650, 2.494, 2.380, 2.294, 2.225, 2.170, 2.123 },
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{ 4.121, 3.267, 2.874, 2.641, 2.485, 2.372, 2.285, 2.217, 2.161, 2.114 },
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{ 4.113, 3.259, 2.866, 2.634, 2.477, 2.364, 2.277, 2.209, 2.153, 2.106 },
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{ 4.105, 3.252, 2.859, 2.626, 2.470, 2.356, 2.270, 2.201, 2.145, 2.098 },
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{ 4.098, 3.245, 2.852, 2.619, 2.463, 2.349, 2.262, 2.194, 2.138, 2.091 },
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{ 4.091, 3.238, 2.845, 2.612, 2.456, 2.342, 2.255, 2.187, 2.131, 2.084 },
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{ 4.085, 3.232, 2.839, 2.606, 2.449, 2.336, 2.249, 2.180, 2.124, 2.077 },
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{ 4.079, 3.226, 2.833, 2.600, 2.443, 2.330, 2.243, 2.174, 2.118, 2.071 },
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{ 4.073, 3.220, 2.827, 2.594, 2.438, 2.324, 2.237, 2.168, 2.112, 2.065 },
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{ 4.067, 3.214, 2.822, 2.589, 2.432, 2.318, 2.232, 2.163, 2.106, 2.059 },
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{ 4.062, 3.209, 2.816, 2.584, 2.427, 2.313, 2.226, 2.157, 2.101, 2.054 },
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{ 4.057, 3.204, 2.812, 2.579, 2.422, 2.308, 2.221, 2.152, 2.096, 2.049 },
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{ 4.052, 3.200, 2.807, 2.574, 2.417, 2.304, 2.216, 2.147, 2.091, 2.044 },
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{ 4.047, 3.195, 2.802, 2.570, 2.413, 2.299, 2.212, 2.143, 2.086, 2.039 },
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{ 4.043, 3.191, 2.798, 2.565, 2.409, 2.295, 2.207, 2.138, 2.082, 2.035 },
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{ 4.038, 3.187, 2.794, 2.561, 2.404, 2.290, 2.203, 2.134, 2.077, 2.030 },
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{ 4.034, 3.183, 2.790, 2.557, 2.400, 2.286, 2.199, 2.130, 2.073, 2.026 },
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{ 4.030, 3.179, 2.786, 2.553, 2.397, 2.283, 2.195, 2.126, 2.069, 2.022 },
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{ 4.027, 3.175, 2.783, 2.550, 2.393, 2.279, 2.192, 2.122, 2.066, 2.018 },
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{ 4.023, 3.172, 2.779, 2.546, 2.389, 2.275, 2.188, 2.119, 2.062, 2.015 },
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{ 4.020, 3.168, 2.776, 2.543, 2.386, 2.272, 2.185, 2.115, 2.059, 2.011 },
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{ 4.016, 3.165, 2.773, 2.540, 2.383, 2.269, 2.181, 2.112, 2.055, 2.008 },
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{ 4.013, 3.162, 2.769, 2.537, 2.380, 2.266, 2.178, 2.109, 2.052, 2.005 },
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{ 4.010, 3.159, 2.766, 2.534, 2.377, 2.263, 2.175, 2.106, 2.049, 2.001 },
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{ 4.007, 3.156, 2.764, 2.531, 2.374, 2.260, 2.172, 2.103, 2.046, 1.998 },
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{ 4.004, 3.153, 2.761, 2.528, 2.371, 2.257, 2.169, 2.100, 2.043, 1.995 },
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{ 4.001, 3.150, 2.758, 2.525, 2.368, 2.254, 2.167, 2.097, 2.040, 1.993 },
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{ 3.998, 3.148, 2.755, 2.523, 2.366, 2.251, 2.164, 2.094, 2.037, 1.990 },
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{ 3.996, 3.145, 2.753, 2.520, 2.363, 2.249, 2.161, 2.092, 2.035, 1.987 },
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{ 3.993, 3.143, 2.751, 2.518, 2.361, 2.246, 2.159, 2.089, 2.032, 1.985 },
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{ 3.991, 3.140, 2.748, 2.515, 2.358, 2.244, 2.156, 2.087, 2.030, 1.982 },
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{ 3.989, 3.138, 2.746, 2.513, 2.356, 2.242, 2.154, 2.084, 2.027, 1.980 },
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{ 3.986, 3.136, 2.744, 2.511, 2.354, 2.239, 2.152, 2.082, 2.025, 1.977 },
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{ 3.984, 3.134, 2.742, 2.509, 2.352, 2.237, 2.150, 2.080, 2.023, 1.975 },
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{ 3.982, 3.132, 2.740, 2.507, 2.350, 2.235, 2.148, 2.078, 2.021, 1.973 },
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{ 3.980, 3.130, 2.737, 2.505, 2.348, 2.233, 2.145, 2.076, 2.019, 1.971 },
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{ 3.978, 3.128, 2.736, 2.503, 2.346, 2.231, 2.143, 2.074, 2.017, 1.969 },
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{ 3.976, 3.126, 2.734, 2.501, 2.344, 2.229, 2.142, 2.072, 2.015, 1.967 },
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{ 3.974, 3.124, 2.732, 2.499, 2.342, 2.227, 2.140, 2.070, 2.013, 1.965 },
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{ 3.972, 3.122, 2.730, 2.497, 2.340, 2.226, 2.138, 2.068, 2.011, 1.963 },
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{ 3.970, 3.120, 2.728, 2.495, 2.338, 2.224, 2.136, 2.066, 2.009, 1.961 },
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{ 3.968, 3.119, 2.727, 2.494, 2.337, 2.222, 2.134, 2.064, 2.007, 1.959 },
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{ 3.967, 3.117, 2.725, 2.492, 2.335, 2.220, 2.133, 2.063, 2.006, 1.958 },
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{ 3.965, 3.115, 2.723, 2.490, 2.333, 2.219, 2.131, 2.061, 2.004, 1.956 },
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{ 3.963, 3.114, 2.722, 2.489, 2.332, 2.217, 2.129, 2.059, 2.002, 1.954 },
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{ 3.962, 3.112, 2.720, 2.487, 2.330, 2.216, 2.128, 2.058, 2.001, 1.953 },
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{ 3.960, 3.111, 2.719, 2.486, 2.329, 2.214, 2.126, 2.056, 1.999, 1.951 },
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{ 3.959, 3.109, 2.717, 2.484, 2.327, 2.213, 2.125, 2.055, 1.998, 1.950 },
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{ 3.957, 3.108, 2.716, 2.483, 2.326, 2.211, 2.123, 2.053, 1.996, 1.948 },
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{ 3.956, 3.107, 2.715, 2.482, 2.324, 2.210, 2.122, 2.052, 1.995, 1.947 },
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{ 3.955, 3.105, 2.713, 2.480, 2.323, 2.209, 2.121, 2.051, 1.993, 1.945 },
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{ 3.953, 3.104, 2.712, 2.479, 2.322, 2.207, 2.119, 2.049, 1.992, 1.944 },
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{ 3.952, 3.103, 2.711, 2.478, 2.321, 2.206, 2.118, 2.048, 1.991, 1.943 },
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{ 3.951, 3.101, 2.709, 2.476, 2.319, 2.205, 2.117, 2.047, 1.989, 1.941 },
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{ 3.949, 3.100, 2.708, 2.475, 2.318, 2.203, 2.115, 2.045, 1.988, 1.940 },
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{ 3.948, 3.099, 2.707, 2.474, 2.317, 2.202, 2.114, 2.044, 1.987, 1.939 },
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{ 3.947, 3.098, 2.706, 2.473, 2.316, 2.201, 2.113, 2.043, 1.986, 1.938 },
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{ 3.946, 3.097, 2.705, 2.472, 2.315, 2.200, 2.112, 2.042, 1.984, 1.936 },
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{ 3.945, 3.095, 2.704, 2.471, 2.313, 2.199, 2.111, 2.041, 1.983, 1.935 },
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{ 3.943, 3.094, 2.703, 2.470, 2.312, 2.198, 2.110, 2.040, 1.982, 1.934 },
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{ 3.942, 3.093, 2.701, 2.469, 2.311, 2.197, 2.109, 2.038, 1.981, 1.933 },
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{ 3.941, 3.092, 2.700, 2.467, 2.310, 2.196, 2.108, 2.037, 1.980, 1.932 },
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{ 3.940, 3.091, 2.699, 2.466, 2.309, 2.195, 2.106, 2.036, 1.979, 1.931 },
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{ 3.939, 3.090, 2.698, 2.465, 2.308, 2.194, 2.105, 2.035, 1.978, 1.930 },
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{ 3.938, 3.089, 2.697, 2.465, 2.307, 2.193, 2.104, 2.034, 1.977, 1.929 },
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{ 3.937, 3.088, 2.696, 2.464, 2.306, 2.192, 2.103, 2.033, 1.976, 1.928 },
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{ 3.936, 3.087, 2.696, 2.463, 2.305, 2.191, 2.103, 2.032, 1.975, 1.927 }
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};
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template <class RealType> // Any floating-point type RealType.
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void test_spots(RealType)
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{
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// Basic sanity checks, test data is to three decimal places only
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// so set tolerance to 0.002 expressed as a persentage. Note that
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// we can't even get full 3 digit accuracy since the data we're
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// using as input has *already been rounded*, leading to even
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// greater differences in output. As an accuracy test this is
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// pretty useless, but it is an excellent sanity check.
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RealType tolerance = 0.002f * 100;
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cout << "Tolerance = " << tolerance << "%." << endl;
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using boost::math::fisher_f_distribution;
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using ::boost::math::fisher_f;
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using ::boost::math::cdf;
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using ::boost::math::pdf;
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for(unsigned i = 0; i < sizeof(upper_critical_values) / sizeof(upper_critical_values[0]); ++i)
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{
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for(unsigned j = 0; j < sizeof(upper_critical_values[0])/sizeof(upper_critical_values[0][0]); ++j)
|
||
|
|
{
|
||
|
|
test_spot(
|
||
|
|
static_cast<RealType>(j+1), // degrees of freedom 1
|
||
|
|
static_cast<RealType>(i+1), // degrees of freedom 2
|
||
|
|
static_cast<RealType>(upper_critical_values[i][j]), // test statistic F
|
||
|
|
static_cast<RealType>(0.95), // Probability of result (CDF), P
|
||
|
|
static_cast<RealType>(0.05), // Q = 1 - P
|
||
|
|
tolerance);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// http://www.vias.org/simulations/simusoft_distcalc.html
|
||
|
|
// Distcalc version 1.2 Copyright 2002 H Lohninger, TU Wein
|
||
|
|
// H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8
|
||
|
|
// The Windows calculator is available zipped distcalc.exe for download at:
|
||
|
|
// http://www.vias.org/simulations/simu_stat.html
|
||
|
|
|
||
|
|
// This interactive Windows program was used to find some combination for which the
|
||
|
|
// result appears to be exact. No doubt this can be done analytically too,
|
||
|
|
// by mathematicians!
|
||
|
|
|
||
|
|
// Some combinations for which the result is 'exact', or at least is to 40 decimal digits.
|
||
|
|
// 40 decimal digits includes 128-bit significand User Defined Floating-Point types.
|
||
|
|
// These all pass tests at near epsilon accuracy for the floating-point type.
|
||
|
|
tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100;
|
||
|
|
cout << "Tolerance = " << tolerance << "%." << endl;
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(1.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(2.)/static_cast<RealType>(3.) ), // F
|
||
|
|
static_cast<RealType>(0.5), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(1.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(1.6L))), // F
|
||
|
|
static_cast<RealType>(0.333333333333333333333333333333333333L), // probability.
|
||
|
|
tolerance * 100); // needs higher tolerance at 128-bit precision - value not exact?
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(1.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(6.5333333333333333333333333333333333L))), // F
|
||
|
|
static_cast<RealType>(0.125L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(1.))), // F
|
||
|
|
static_cast<RealType>(0.5L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(3.))), // F
|
||
|
|
static_cast<RealType>(0.25L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(3.))), // F
|
||
|
|
static_cast<RealType>(0.25L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(7.))), // F
|
||
|
|
static_cast<RealType>(0.125L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(9.))), // F
|
||
|
|
static_cast<RealType>(0.1L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(19.))), // F
|
||
|
|
static_cast<RealType>(0.05L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(29.))), // F
|
||
|
|
static_cast<RealType>(0.03333333333333333333333333333333333333333L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(99.))), // F
|
||
|
|
static_cast<RealType>(0.01L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(4.), // df1
|
||
|
|
static_cast<RealType>(4.)), // df2
|
||
|
|
static_cast<RealType>(9.))), // F
|
||
|
|
static_cast<RealType>(0.028L), // probability.
|
||
|
|
tolerance*10); // not quite exact???
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(8.), // df1
|
||
|
|
static_cast<RealType>(8.)), // df2
|
||
|
|
static_cast<RealType>(1.))), // F
|
||
|
|
static_cast<RealType>(0.5L), // probability.
|
||
|
|
tolerance);
|
||
|
|
|
||
|
|
// Inverse tests
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
quantile(complement(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(0.03333333333333333333333333333333333333333L))), // probability
|
||
|
|
static_cast<RealType>(29.), // F expected.
|
||
|
|
tolerance*10);
|
||
|
|
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
quantile(fisher_f_distribution<RealType>(
|
||
|
|
static_cast<RealType>(2.), // df1
|
||
|
|
static_cast<RealType>(2.)), // df2
|
||
|
|
static_cast<RealType>(1.0L - 0.03333333333333333333333333333333333333333L)), // probability
|
||
|
|
static_cast<RealType>(29.), // F expected.
|
||
|
|
tolerance*10);
|
||
|
|
|
||
|
|
|
||
|
|
// Also note limit cases for F(1, infinity) == normal distribution
|
||
|
|
// F(1, n2) == Student's t distribution
|
||
|
|
// F(n1, infinity) == Chisq distribution
|
||
|
|
|
||
|
|
// These might allow some further cross checks?
|
||
|
|
|
||
|
|
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percent
|
||
|
|
cout << "Tolerance = " << tol2 << "%." << endl;
|
||
|
|
fisher_f_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(6));
|
||
|
|
RealType x = 7;
|
||
|
|
using namespace std; // ADL of std names.
|
||
|
|
// mean:
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
mean(dist)
|
||
|
|
, static_cast<RealType>(6)/static_cast<RealType>(4), tol2);
|
||
|
|
// variance:
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
variance(dist)
|
||
|
|
, static_cast<RealType>(2 * 6 * 6 * (8 + 6 - 2)) / static_cast<RealType>(8 * 16 * 2), tol2);
|
||
|
|
// std deviation:
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
standard_deviation(dist)
|
||
|
|
, sqrt(static_cast<RealType>(2 * 6 * 6 * (8 + 6 - 2)) / static_cast<RealType>(8 * 16 * 2)), tol2);
|
||
|
|
// hazard:
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
hazard(dist, x)
|
||
|
|
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
|
||
|
|
// cumulative hazard:
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
chf(dist, x)
|
||
|
|
, -log(cdf(complement(dist, x))), tol2);
|
||
|
|
// coefficient_of_variation:
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
coefficient_of_variation(dist)
|
||
|
|
, standard_deviation(dist) / mean(dist), tol2);
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
mode(dist)
|
||
|
|
, static_cast<RealType>(6*6)/static_cast<RealType>(8*8), tol2);
|
||
|
|
|
||
|
|
fisher_f_distribution<RealType> dist2(static_cast<RealType>(8), static_cast<RealType>(12));
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
skewness(dist2)
|
||
|
|
, static_cast<RealType>(26 * sqrt(64.0L)) / (12*6), tol2);
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
kurtosis_excess(dist2)
|
||
|
|
, static_cast<RealType>(6272) * 12 / 3456, tol2);
|
||
|
|
BOOST_CHECK_CLOSE(
|
||
|
|
kurtosis(dist2)
|
||
|
|
, static_cast<RealType>(6272) * 12 / 3456 + 3, tol2);
|
||
|
|
// special cases:
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
pdf(
|
||
|
|
fisher_f_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
|
||
|
|
static_cast<RealType>(0)), std::overflow_error
|
||
|
|
);
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
pdf(fisher_f_distribution<RealType>(2, 2), static_cast<RealType>(0))
|
||
|
|
, static_cast<RealType>(1.0f));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
pdf(fisher_f_distribution<RealType>(3, 3), static_cast<RealType>(0))
|
||
|
|
, static_cast<RealType>(0.0f));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
cdf(fisher_f_distribution<RealType>(1, 1), static_cast<RealType>(0))
|
||
|
|
, static_cast<RealType>(0.0f));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
cdf(fisher_f_distribution<RealType>(2, 2), static_cast<RealType>(0))
|
||
|
|
, static_cast<RealType>(0.0f));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
cdf(fisher_f_distribution<RealType>(3, 3), static_cast<RealType>(0))
|
||
|
|
, static_cast<RealType>(0.0f));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(1, 1), static_cast<RealType>(0)))
|
||
|
|
, static_cast<RealType>(1));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(2, 2), static_cast<RealType>(0)))
|
||
|
|
, static_cast<RealType>(1));
|
||
|
|
BOOST_CHECK_EQUAL(
|
||
|
|
cdf(complement(fisher_f_distribution<RealType>(3, 3), static_cast<RealType>(0)))
|
||
|
|
, static_cast<RealType>(1));
|
||
|
|
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
pdf(
|
||
|
|
fisher_f_distribution<RealType>(-1, 2),
|
||
|
|
static_cast<RealType>(1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
pdf(
|
||
|
|
fisher_f_distribution<RealType>(1, -1),
|
||
|
|
static_cast<RealType>(1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
pdf(
|
||
|
|
fisher_f_distribution<RealType>(8, 2),
|
||
|
|
static_cast<RealType>(-1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
cdf(
|
||
|
|
fisher_f_distribution<RealType>(-1, 1),
|
||
|
|
static_cast<RealType>(1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
cdf(
|
||
|
|
fisher_f_distribution<RealType>(8, 4),
|
||
|
|
static_cast<RealType>(-1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
cdf(complement(
|
||
|
|
fisher_f_distribution<RealType>(-1, 2),
|
||
|
|
static_cast<RealType>(1))), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
cdf(complement(
|
||
|
|
fisher_f_distribution<RealType>(8, 4),
|
||
|
|
static_cast<RealType>(-1))), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
quantile(
|
||
|
|
fisher_f_distribution<RealType>(-1, 2),
|
||
|
|
static_cast<RealType>(0.5)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
quantile(
|
||
|
|
fisher_f_distribution<RealType>(8, 8),
|
||
|
|
static_cast<RealType>(-1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
quantile(
|
||
|
|
fisher_f_distribution<RealType>(8, 8),
|
||
|
|
static_cast<RealType>(1.1)), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
quantile(complement(
|
||
|
|
fisher_f_distribution<RealType>(2, -1),
|
||
|
|
static_cast<RealType>(0.5))), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
quantile(complement(
|
||
|
|
fisher_f_distribution<RealType>(8, 8),
|
||
|
|
static_cast<RealType>(-1))), std::domain_error
|
||
|
|
);
|
||
|
|
BOOST_MATH_CHECK_THROW(
|
||
|
|
quantile(complement(
|
||
|
|
fisher_f_distribution<RealType>(8, 8),
|
||
|
|
static_cast<RealType>(1.1))), std::domain_error
|
||
|
|
);
|
||
|
|
check_out_of_range<fisher_f_distribution<RealType> >(2, 3);
|
||
|
|
} // template <class RealType>void test_spots(RealType)
|
||
|
|
|
||
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
||
|
|
{
|
||
|
|
|
||
|
|
// Check that can generate fisher distribution using the two convenience methods:
|
||
|
|
boost::math::fisher_f myf1(1., 2); // Using typedef
|
||
|
|
fisher_f_distribution<> myf2(1., 2); // Using default RealType double.
|
||
|
|
|
||
|
|
|
||
|
|
// Basic sanity-check spot values.
|
||
|
|
|
||
|
|
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
||
|
|
test_spots(0.0F); // Test float.
|
||
|
|
test_spots(0.0); // Test double.
|
||
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
||
|
|
test_spots(0.0L); // Test long double.
|
||
|
|
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
|
||
|
|
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
|
||
|
|
} // BOOST_AUTO_TEST_CASE( test_main )
|
||
|
|
|
||
|
|
/*
|
||
|
|
|
||
|
|
Output is:
|
||
|
|
|
||
|
|
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_fisher.exe"
|
||
|
|
Running 1 test case...
|
||
|
|
Tolerance = 0.2%.
|
||
|
|
Tolerance = 5.96046e-005%.
|
||
|
|
Tolerance = 5.96046e-005%.
|
||
|
|
Tolerance = 0.2%.
|
||
|
|
Tolerance = 1.11022e-013%.
|
||
|
|
Tolerance = 1.11022e-013%.
|
||
|
|
Tolerance = 0.2%.
|
||
|
|
Tolerance = 1.11022e-013%.
|
||
|
|
Tolerance = 1.11022e-013%.
|
||
|
|
Tolerance = 0.2%.
|
||
|
|
Tolerance = 1.11022e-013%.
|
||
|
|
Tolerance = 1.11022e-013%.
|
||
|
|
*** No errors detected
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
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|