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651 lines
26 KiB
C++
651 lines
26 KiB
C++
// test_poisson.cpp
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// Copyright Paul A. Bristow 2007.
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// Copyright John Maddock 2006.
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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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// Basic sanity test for Poisson Cumulative Distribution Function.
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#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
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#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
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# define TEST_FLOAT
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# define TEST_DOUBLE
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# define TEST_LDOUBLE
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# define TEST_REAL_CONCEPT
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#endif
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#ifdef _MSC_VER
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# pragma warning(disable: 4127) // conditional expression is constant.
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#endif
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#include <boost/math/distributions/poisson.hpp>
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using boost::math::poisson_distribution;
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#include <boost/math/tools/test.hpp> // for real_concept
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#include <boost/math/special_functions/gamma.hpp> // for (incomplete) gamma.
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// using boost::math::qamma_Q;
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#include "table_type.hpp"
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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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using std::setprecision;
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using std::showpoint;
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using std::ios;
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#include <limits>
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using std::numeric_limits;
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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, tolerance is about numeric_limits<RealType>::digits10 decimal places,
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// guaranteed for type RealType, eg 6 for float, 15 for double,
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// expressed as a percentage (so -2) for BOOST_CHECK_CLOSE,
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int decdigits = numeric_limits<RealType>::digits10;
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// May eb >15 for 80 and 128-bit FP typtes.
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if (decdigits <= 0)
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{ // decdigits is not defined, for example real concept,
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// so assume precision of most test data is double (for example, MathCAD).
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decdigits = numeric_limits<double>::digits10; // == 15 for 64-bit
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}
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if (decdigits > 15 ) // numeric_limits<double>::digits10)
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{ // 15 is the accuracy of the MathCAD test data.
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decdigits = 15; // numeric_limits<double>::digits10;
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}
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decdigits -= 1; // Perhaps allow some decimal digit(s) margin of numerical error.
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RealType tolerance = static_cast<RealType>(std::pow(10., static_cast<double>(2-decdigits))); // 1e-6 (-2 so as %)
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tolerance *= 2; // Allow some bit(s) small margin (2 means + or - 1 bit) of numerical error.
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// Typically 2e-13% = 2e-15 as fraction for double.
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// Sources of spot test values:
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// Many be some combinations for which the result is 'exact',
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// or at least is good to 40 decimal digits.
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// 40 decimal digits includes 128-bit significand User Defined Floating-Point types,
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// Best source of accurate values is:
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// Mathworld online calculator (40 decimal digits precision, suitable for up to 128-bit significands)
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// http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=GammaRegularized
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// GammaRegularized is same as gamma incomplete, gamma or gamma_q(a, x) or Q(a, z).
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// http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/PoissonDistribution.html
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// MathCAD defines ppois(k, lambda== mean) as k integer, k >=0.
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// ppois(0, 5) = 6.73794699908547e-3
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// ppois(1, 5) = 0.040427681994513;
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// ppois(10, 10) = 5.830397501929850E-001
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// ppois(10, 1) = 9.999999899522340E-001
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// ppois(5,5) = 0.615960654833065
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// qpois returns inverse Poission distribution, that is the smallest (floor) k so that ppois(k, lambda) >= p
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// p is real number, real mean lambda > 0
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// k is approximately the integer for which probability(X <= k) = p
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// when random variable X has the Poisson distribution with parameters lambda.
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// Uses discrete bisection.
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// qpois(6.73794699908547e-3, 5) = 1
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// qpois(0.040427681994513, 5) =
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// Test Poisson with spot values from MathCAD 'known good'.
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using boost::math::poisson_distribution;
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using ::boost::math::poisson;
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using ::boost::math::cdf;
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using ::boost::math::pdf;
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// Check that bad arguments throw.
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BOOST_MATH_CHECK_THROW(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
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static_cast<RealType>(0)), // even for a good k.
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std::domain_error); // Expected error to be thrown.
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BOOST_MATH_CHECK_THROW(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(-1)), // mean negative is bad.
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static_cast<RealType>(0)),
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unit OK,
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static_cast<RealType>(-1)), // but negative events is bad.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
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static_cast<RealType>(99999)), // for any k events.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
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static_cast<RealType>(99999)), // for any k events.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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quantile(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero.
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static_cast<RealType>(0.5)), // probability OK.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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quantile(poisson_distribution<RealType>(static_cast<RealType>(-1)),
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static_cast<RealType>(-1)), // bad probability.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
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static_cast<RealType>(-1)), // bad probability.
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std::domain_error);
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BOOST_MATH_CHECK_THROW(
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quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
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static_cast<RealType>(1)), // bad probability.
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std::overflow_error);
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BOOST_MATH_CHECK_THROW(
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quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)),
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static_cast<RealType>(0))), // bad probability.
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std::overflow_error);
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BOOST_CHECK_EQUAL(
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quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
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static_cast<RealType>(0)), // bad probability.
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0);
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BOOST_CHECK_EQUAL(
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quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)),
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static_cast<RealType>(1))), // bad probability.
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0);
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// Check some test values.
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BOOST_CHECK_CLOSE( // mode
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mode(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
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static_cast<RealType>(4), // mode.
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tolerance);
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//BOOST_CHECK_CLOSE( // mode
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// median(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
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// static_cast<RealType>(4), // mode.
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// tolerance);
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poisson_distribution<RealType> dist4(static_cast<RealType>(40));
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BOOST_CHECK_CLOSE( // median
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median(dist4), // mode = mean = 4. median = 40.328333333333333
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quantile(dist4, static_cast<RealType>(0.5)), // 39.332839138842637
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tolerance);
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// PDF
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BOOST_CHECK_CLOSE(
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pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
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static_cast<RealType>(0)),
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static_cast<RealType>(1.831563888873410E-002), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
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static_cast<RealType>(2)),
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static_cast<RealType>(1.465251111098740E-001), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(poisson_distribution<RealType>(static_cast<RealType>(20)), // mean big.
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static_cast<RealType>(1)), // k small
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static_cast<RealType>(4.122307244877130E-008), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
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static_cast<RealType>(20)), // K>> mean
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static_cast<RealType>(8.277463646553730E-009), // probability.
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tolerance);
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// CDF
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(0)), // zero k events.
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static_cast<RealType>(3.678794411714420E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(1)), // one k event.
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static_cast<RealType>(7.357588823428830E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(2)), // two k events.
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static_cast<RealType>(9.196986029286060E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(10)), // two k events.
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static_cast<RealType>(9.999999899522340E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(15)), // two k events.
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static_cast<RealType>(9.999999999999810E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(16)), // two k events.
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static_cast<RealType>(9.999999999999990E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(17)), // two k events.
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static_cast<RealType>(1.), // probability unity for double.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(33)), // k events at limit for float unchecked_factorial table.
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static_cast<RealType>(1.), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(100)), // mean 100.
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static_cast<RealType>(33)), // k events at limit for float unchecked_factorial table.
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static_cast<RealType>(6.328271240363390E-15), // probability is tiny.
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tolerance * static_cast<RealType>(2e11)); // 6.3495253382825722e-015 MathCAD
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// Note that there two tiny probability are much more different.
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(100)), // mean 100.
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static_cast<RealType>(34)), // k events at limit for float unchecked_factorial table.
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static_cast<RealType>(1.898481372109020E-14), // probability is tiny.
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tolerance*static_cast<RealType>(2e11)); // 1.8984813721090199e-014 MathCAD
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(33)), // mean = k
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static_cast<RealType>(33)), // k events above limit for float unchecked_factorial table.
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static_cast<RealType>(5.461191812386560E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(33)), // mean = k-1
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static_cast<RealType>(34)), // k events above limit for float unchecked_factorial table.
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static_cast<RealType>(6.133535681502950E-1), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
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static_cast<RealType>(34)), // k events above limit for float unchecked_factorial table.
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static_cast<RealType>(1.), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
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static_cast<RealType>(5)), // k events.
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static_cast<RealType>(0.615960654833065), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
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static_cast<RealType>(1)), // k events.
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static_cast<RealType>(0.040427681994512805), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
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static_cast<RealType>(0)), // k events (uses special case formula, not gamma).
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static_cast<RealType>(0.006737946999085467), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(1.)), // mean
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static_cast<RealType>(0)), // k events (uses special case formula, not gamma).
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static_cast<RealType>(0.36787944117144233), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
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static_cast<RealType>(10)), // k events.
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static_cast<RealType>(0.5830397501929856), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
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static_cast<RealType>(5)), // k events.
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static_cast<RealType>(0.785130387030406), // probability.
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tolerance);
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// complement CDF
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BOOST_CHECK_CLOSE( // Complement CDF
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cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
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static_cast<RealType>(5))), // k events.
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static_cast<RealType>(1 - 0.785130387030406), // probability.
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tolerance);
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BOOST_CHECK_CLOSE( // Complement CDF
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cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
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static_cast<RealType>(0))), // Zero k events (uses special case formula, not gamma).
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static_cast<RealType>(0.98168436111126578), // probability.
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tolerance);
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BOOST_CHECK_CLOSE( // Complement CDF
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cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(1.)), // mean
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static_cast<RealType>(0))), // Zero k events (uses special case formula, not gamma).
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static_cast<RealType>(0.63212055882855767), // probability.
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tolerance);
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// Example where k is bigger than max_factorial (>34 for float)
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// (therefore using log gamma so perhaps less accurate).
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(40.)), // mean
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static_cast<RealType>(40)), // k events.
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static_cast<RealType>(0.5419181783625430), // probability.
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tolerance);
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// Quantile & complement.
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BOOST_CHECK_CLOSE(
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boost::math::quantile(
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poisson_distribution<RealType>(5), // mean.
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static_cast<RealType>(0.615960654833065)), // probability.
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static_cast<RealType>(5.), // Expect k = 5
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tolerance/5); //
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// EQUAL is too optimistic - fails [5.0000000000000124 != 5]
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// BOOST_CHECK_EQUAL(boost::math::quantile( //
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// poisson_distribution<RealType>(5.), // mean.
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// static_cast<RealType>(0.615960654833065)), // probability.
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// static_cast<RealType>(5.)); // Expect k = 5 events.
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BOOST_CHECK_CLOSE(boost::math::quantile(
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poisson_distribution<RealType>(4), // mean.
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static_cast<RealType>(0.785130387030406)), // probability.
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static_cast<RealType>(5.), // Expect k = 5 events.
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tolerance/5);
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// Check on quantile of other examples of inverse of cdf.
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
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static_cast<RealType>(10)), // k events.
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static_cast<RealType>(0.5830397501929856), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
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poisson_distribution<RealType>(10.), // mean.
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static_cast<RealType>(0.5830397501929856)), // probability.
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static_cast<RealType>(10.), // Expect k = 10 events.
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tolerance/5);
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BOOST_CHECK_CLOSE(
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cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
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static_cast<RealType>(5)), // k events.
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static_cast<RealType>(0.785130387030406), // probability.
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tolerance);
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BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
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poisson_distribution<RealType>(4.), // mean.
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static_cast<RealType>(0.785130387030406)), // probability.
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static_cast<RealType>(5.), // Expect k = 10 events.
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tolerance/5);
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//BOOST_CHECK_CLOSE(boost::math::quantile(
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// poisson_distribution<RealType>(5), // mean.
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// static_cast<RealType>(0.785130387030406)), // probability.
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// // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
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// static_cast<RealType>(6.), // Expect k = 6 events.
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// tolerance/5);
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//BOOST_CHECK_CLOSE(boost::math::quantile(
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// poisson_distribution<RealType>(5), // mean.
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// static_cast<RealType>(0.77)), // probability.
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// // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
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// static_cast<RealType>(7.), // Expect k = 6 events.
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// tolerance/5);
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//BOOST_CHECK_CLOSE(boost::math::quantile(
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// poisson_distribution<RealType>(5), // mean.
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// static_cast<RealType>(0.75)), // probability.
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// // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
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// static_cast<RealType>(6.), // Expect k = 6 events.
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// tolerance/5);
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BOOST_CHECK_CLOSE(
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boost::math::quantile(
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complement(
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poisson_distribution<RealType>(4),
|
|
static_cast<RealType>(1 - 0.785130387030406))), // complement.
|
|
static_cast<RealType>(5), // Expect k = 5 events.
|
|
tolerance/5);
|
|
|
|
BOOST_CHECK_EQUAL(boost::math::quantile( // Check case when probability < cdf(0) (== pdf(0))
|
|
poisson_distribution<RealType>(1), // mean is small, so cdf and pdf(0) are about 0.35.
|
|
static_cast<RealType>(0.0001)), // probability < cdf(0).
|
|
static_cast<RealType>(0)); // Expect k = 0 events exactly.
|
|
|
|
BOOST_CHECK_EQUAL(
|
|
boost::math::quantile(
|
|
complement(
|
|
poisson_distribution<RealType>(1),
|
|
static_cast<RealType>(0.9999))), // complement, so 1-probability < cdf(0)
|
|
static_cast<RealType>(0)); // Expect k = 0 events exactly.
|
|
|
|
//
|
|
// Test quantile policies against test data:
|
|
//
|
|
#define T RealType
|
|
#include "poisson_quantile.ipp"
|
|
|
|
for(unsigned i = 0; i < poisson_quantile_data.size(); ++i)
|
|
{
|
|
using namespace boost::math::policies;
|
|
typedef policy<discrete_quantile<real> > P1;
|
|
typedef policy<discrete_quantile<integer_round_down> > P2;
|
|
typedef policy<discrete_quantile<integer_round_up> > P3;
|
|
typedef policy<discrete_quantile<integer_round_outwards> > P4;
|
|
typedef policy<discrete_quantile<integer_round_inwards> > P5;
|
|
typedef policy<discrete_quantile<integer_round_nearest> > P6;
|
|
RealType tol = boost::math::tools::epsilon<RealType>() * 20;
|
|
if(!boost::is_floating_point<RealType>::value)
|
|
tol *= 7;
|
|
//
|
|
// Check full real value first:
|
|
//
|
|
poisson_distribution<RealType, P1> p1(poisson_quantile_data[i][0]);
|
|
RealType x = quantile(p1, poisson_quantile_data[i][1]);
|
|
BOOST_CHECK_CLOSE_FRACTION(x, poisson_quantile_data[i][2], tol);
|
|
x = quantile(complement(p1, poisson_quantile_data[i][1]));
|
|
BOOST_CHECK_CLOSE_FRACTION(x, poisson_quantile_data[i][3], tol * 3);
|
|
//
|
|
// Now with round down to integer:
|
|
//
|
|
poisson_distribution<RealType, P2> p2(poisson_quantile_data[i][0]);
|
|
x = quantile(p2, poisson_quantile_data[i][1]);
|
|
BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][2]));
|
|
x = quantile(complement(p2, poisson_quantile_data[i][1]));
|
|
BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][3]));
|
|
//
|
|
// Now with round up to integer:
|
|
//
|
|
poisson_distribution<RealType, P3> p3(poisson_quantile_data[i][0]);
|
|
x = quantile(p3, poisson_quantile_data[i][1]);
|
|
BOOST_CHECK_EQUAL(x, ceil(poisson_quantile_data[i][2]));
|
|
x = quantile(complement(p3, poisson_quantile_data[i][1]));
|
|
BOOST_CHECK_EQUAL(x, ceil(poisson_quantile_data[i][3]));
|
|
//
|
|
// Now with round to integer "outside":
|
|
//
|
|
poisson_distribution<RealType, P4> p4(poisson_quantile_data[i][0]);
|
|
x = quantile(p4, poisson_quantile_data[i][1]);
|
|
BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? floor(poisson_quantile_data[i][2]) : ceil(poisson_quantile_data[i][2]));
|
|
x = quantile(complement(p4, poisson_quantile_data[i][1]));
|
|
BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? ceil(poisson_quantile_data[i][3]) : floor(poisson_quantile_data[i][3]));
|
|
//
|
|
// Now with round to integer "inside":
|
|
//
|
|
poisson_distribution<RealType, P5> p5(poisson_quantile_data[i][0]);
|
|
x = quantile(p5, poisson_quantile_data[i][1]);
|
|
BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? ceil(poisson_quantile_data[i][2]) : floor(poisson_quantile_data[i][2]));
|
|
x = quantile(complement(p5, poisson_quantile_data[i][1]));
|
|
BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? floor(poisson_quantile_data[i][3]) : ceil(poisson_quantile_data[i][3]));
|
|
//
|
|
// Now with round to nearest integer:
|
|
//
|
|
poisson_distribution<RealType, P6> p6(poisson_quantile_data[i][0]);
|
|
x = quantile(p6, poisson_quantile_data[i][1]);
|
|
BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][2] + 0.5f));
|
|
x = quantile(complement(p6, poisson_quantile_data[i][1]));
|
|
BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][3] + 0.5f));
|
|
}
|
|
check_out_of_range<poisson_distribution<RealType> >(1);
|
|
} // template <class RealType>void test_spots(RealType)
|
|
|
|
//
|
|
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
|
{
|
|
// Check that can construct normal distribution using the two convenience methods:
|
|
using namespace boost::math;
|
|
poisson myp1(2); // Using typedef
|
|
poisson_distribution<> myp2(2); // Using default RealType double.
|
|
|
|
// Basic sanity-check spot values.
|
|
|
|
// Some plain double examples & tests:
|
|
cout.precision(17); // double max_digits10
|
|
cout.setf(ios::showpoint);
|
|
|
|
poisson mypoisson(4.); // // mean = 4, default FP type is double.
|
|
cout << "mean(mypoisson, 4.) == " << mean(mypoisson) << endl;
|
|
cout << "mean(mypoisson, 0.) == " << mean(mypoisson) << endl;
|
|
cout << "cdf(mypoisson, 2.) == " << cdf(mypoisson, 2.) << endl;
|
|
cout << "pdf(mypoisson, 2.) == " << pdf(mypoisson, 2.) << endl;
|
|
|
|
// poisson mydudpoisson(0.);
|
|
// throws (if BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error).
|
|
|
|
#ifndef BOOST_NO_EXCEPTIONS
|
|
BOOST_MATH_CHECK_THROW(poisson mydudpoisson(-1), std::domain_error);// Mean must be > 0.
|
|
BOOST_MATH_CHECK_THROW(poisson mydudpoisson(-1), std::logic_error);// Mean must be > 0.
|
|
#else
|
|
BOOST_MATH_CHECK_THROW(poisson(-1), std::domain_error);// Mean must be > 0.
|
|
BOOST_MATH_CHECK_THROW(poisson(-1), std::logic_error);// Mean must be > 0.
|
|
#endif
|
|
// Passes the check because logic_error is a parent????
|
|
// BOOST_MATH_CHECK_THROW(poisson mydudpoisson(-1), std::overflow_error); // fails the check
|
|
// because overflow_error is unrelated - except from std::exception
|
|
BOOST_MATH_CHECK_THROW(cdf(mypoisson, -1), std::domain_error); // k must be >= 0
|
|
|
|
BOOST_CHECK_EQUAL(mean(mypoisson), 4.);
|
|
BOOST_CHECK_CLOSE(
|
|
pdf(mypoisson, 2.), // k events = 2.
|
|
1.465251111098740E-001, // probability.
|
|
5e-13);
|
|
|
|
BOOST_CHECK_CLOSE(
|
|
cdf(mypoisson, 2.), // k events = 2.
|
|
0.238103305553545, // probability.
|
|
5e-13);
|
|
|
|
|
|
#if 0
|
|
// Compare cdf from finite sum of pdf and gamma_q.
|
|
using boost::math::cdf;
|
|
using boost::math::pdf;
|
|
|
|
double mean = 4.;
|
|
cout.precision(17); // double max_digits10
|
|
cout.setf(ios::showpoint);
|
|
cout << showpoint << endl; // Ensure trailing zeros are shown.
|
|
// This also helps show the expected precision max_digits10
|
|
//cout.unsetf(ios::showpoint); // No trailing zeros are shown.
|
|
|
|
cout << "k pdf sum cdf diff" << endl;
|
|
double sum = 0.;
|
|
for (int i = 0; i <= 50; i++)
|
|
{
|
|
cout << i << ' ' ;
|
|
double p = pdf(poisson_distribution<double>(mean), static_cast<double>(i));
|
|
sum += p;
|
|
|
|
cout << p << ' ' << sum << ' '
|
|
<< cdf(poisson_distribution<double>(mean), static_cast<double>(i)) << ' ';
|
|
{
|
|
cout << boost::math::gamma_q<double>(i+1, mean); // cdf
|
|
double diff = boost::math::gamma_q<double>(i+1, mean) - sum; // cdf -sum
|
|
cout << setprecision (2) << ' ' << diff; // 0 0 to 4, 1 eps 5 to 9, 10 to 20 2 eps, 21 upwards 3 eps
|
|
|
|
}
|
|
BOOST_CHECK_CLOSE(
|
|
cdf(mypoisson, static_cast<double>(i)),
|
|
sum, // of pdfs.
|
|
4e-14); // Fails at 2e-14
|
|
// This call puts the precision etc back to default 6 !!!
|
|
cout << setprecision(17) << showpoint;
|
|
|
|
|
|
cout << endl;
|
|
}
|
|
|
|
cout << cdf(poisson_distribution<double>(5), static_cast<double>(0)) << ' ' << endl; // 0.006737946999085467
|
|
cout << cdf(poisson_distribution<double>(5), static_cast<double>(1)) << ' ' << endl; // 0.040427681994512805
|
|
cout << cdf(poisson_distribution<double>(2), static_cast<double>(3)) << ' ' << endl; // 0.85712346049854715
|
|
|
|
{ // Compare approximate formula in Wikipedia with quantile(half)
|
|
for (int i = 1; i < 100; i++)
|
|
{
|
|
poisson_distribution<double> distn(static_cast<double>(i));
|
|
cout << i << ' ' << median(distn) << ' ' << quantile(distn, 0.5) << ' '
|
|
<< median(distn) - quantile(distn, 0.5) << endl; // formula appears to be out-by-one??
|
|
} // so quantile(half) used via derived accressors.
|
|
}
|
|
#endif
|
|
|
|
// (Parameter value, arbitrarily zero, only communicates the floating-point type).
|
|
#ifdef TEST_POISSON
|
|
test_spots(0.0F); // Test float.
|
|
#endif
|
|
#ifdef TEST_DOUBLE
|
|
test_spots(0.0); // Test double.
|
|
#endif
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
if (numeric_limits<long double>::digits10 > numeric_limits<double>::digits10)
|
|
{ // long double is better than double (so not MSVC where they are same).
|
|
#ifdef TEST_LDOUBLE
|
|
test_spots(0.0L); // Test long double.
|
|
#endif
|
|
}
|
|
|
|
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
|
|
#ifdef TEST_REAL_CONCEPT
|
|
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
|
|
#endif
|
|
#endif
|
|
#endif
|
|
|
|
} // BOOST_AUTO_TEST_CASE( test_main )
|
|
|
|
/*
|
|
|
|
Output:
|
|
|
|
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_poisson.exe"
|
|
Running 1 test case...
|
|
mean(mypoisson, 4.) == 4.0000000000000000
|
|
mean(mypoisson, 0.) == 4.0000000000000000
|
|
cdf(mypoisson, 2.) == 0.23810330555354431
|
|
pdf(mypoisson, 2.) == 0.14652511110987343
|
|
*** No errors detected
|
|
|
|
*/
|