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// test_poisson.cpp
// Copyright Paul A. Bristow 2007.
// Copyright John Maddock 2006.
// 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)
// Basic sanity test for Poisson Cumulative Distribution Function.
#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
# define TEST_FLOAT
# define TEST_DOUBLE
# define TEST_LDOUBLE
# define TEST_REAL_CONCEPT
#endif
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
#endif
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // Boost.Test
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/distributions/poisson.hpp>
using boost::math::poisson_distribution;
#include <boost/math/tools/test.hpp> // for real_concept
#include <boost/math/special_functions/gamma.hpp> // for (incomplete) gamma.
// using boost::math::qamma_Q;
#include "table_type.hpp"
#include "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
using std::setprecision;
using std::showpoint;
using std::ios;
#include <limits>
using std::numeric_limits;
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
// Basic sanity checks, tolerance is about numeric_limits<RealType>::digits10 decimal places,
// guaranteed for type RealType, eg 6 for float, 15 for double,
// expressed as a percentage (so -2) for BOOST_CHECK_CLOSE,
int decdigits = numeric_limits<RealType>::digits10;
// May eb >15 for 80 and 128-bit FP typtes.
if (decdigits <= 0)
{ // decdigits is not defined, for example real concept,
// so assume precision of most test data is double (for example, MathCAD).
decdigits = numeric_limits<double>::digits10; // == 15 for 64-bit
}
if (decdigits > 15 ) // numeric_limits<double>::digits10)
{ // 15 is the accuracy of the MathCAD test data.
decdigits = 15; // numeric_limits<double>::digits10;
}
decdigits -= 1; // Perhaps allow some decimal digit(s) margin of numerical error.
RealType tolerance = static_cast<RealType>(std::pow(10., static_cast<double>(2-decdigits))); // 1e-6 (-2 so as %)
tolerance *= 2; // Allow some bit(s) small margin (2 means + or - 1 bit) of numerical error.
// Typically 2e-13% = 2e-15 as fraction for double.
// Sources of spot test values:
// Many be some combinations for which the result is 'exact',
// or at least is good to 40 decimal digits.
// 40 decimal digits includes 128-bit significand User Defined Floating-Point types,
// Best source of accurate values is:
// Mathworld online calculator (40 decimal digits precision, suitable for up to 128-bit significands)
// http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=GammaRegularized
// GammaRegularized is same as gamma incomplete, gamma or gamma_q(a, x) or Q(a, z).
// http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/PoissonDistribution.html
// MathCAD defines ppois(k, lambda== mean) as k integer, k >=0.
// ppois(0, 5) = 6.73794699908547e-3
// ppois(1, 5) = 0.040427681994513;
// ppois(10, 10) = 5.830397501929850E-001
// ppois(10, 1) = 9.999999899522340E-001
// ppois(5,5) = 0.615960654833065
// qpois returns inverse Poission distribution, that is the smallest (floor) k so that ppois(k, lambda) >= p
// p is real number, real mean lambda > 0
// k is approximately the integer for which probability(X <= k) = p
// when random variable X has the Poisson distribution with parameters lambda.
// Uses discrete bisection.
// qpois(6.73794699908547e-3, 5) = 1
// qpois(0.040427681994513, 5) =
// Test Poisson with spot values from MathCAD 'known good'.
using boost::math::poisson_distribution;
using ::boost::math::poisson;
using ::boost::math::cdf;
using ::boost::math::pdf;
// Check that bad arguments throw.
BOOST_CHECK_THROW(
cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
static_cast<RealType>(0)), // even for a good k.
std::domain_error); // Expected error to be thrown.
BOOST_CHECK_THROW(
cdf(poisson_distribution<RealType>(static_cast<RealType>(-1)), // mean negative is bad.
static_cast<RealType>(0)),
std::domain_error);
BOOST_CHECK_THROW(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unit OK,
static_cast<RealType>(-1)), // but negative events is bad.
std::domain_error);
BOOST_CHECK_THROW(
cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
static_cast<RealType>(99999)), // for any k events.
std::domain_error);
BOOST_CHECK_THROW(
cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
static_cast<RealType>(99999)), // for any k events.
std::domain_error);
BOOST_CHECK_THROW(
quantile(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero.
static_cast<RealType>(0.5)), // probability OK.
std::domain_error);
BOOST_CHECK_THROW(
quantile(poisson_distribution<RealType>(static_cast<RealType>(-1)),
static_cast<RealType>(-1)), // bad probability.
std::domain_error);
BOOST_CHECK_THROW(
quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(-1)), // bad probability.
std::domain_error);
BOOST_CHECK_THROW(
quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(1)), // bad probability.
std::overflow_error);
BOOST_CHECK_THROW(
quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(0))), // bad probability.
std::overflow_error);
BOOST_CHECK_EQUAL(
quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(0)), // bad probability.
0);
BOOST_CHECK_EQUAL(
quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)),
static_cast<RealType>(1))), // bad probability.
0);
// Check some test values.
BOOST_CHECK_CLOSE( // mode
mode(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
static_cast<RealType>(4), // mode.
tolerance);
//BOOST_CHECK_CLOSE( // mode
// median(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
// static_cast<RealType>(4), // mode.
// tolerance);
poisson_distribution<RealType> dist4(static_cast<RealType>(40));
BOOST_CHECK_CLOSE( // median
median(dist4), // mode = mean = 4. median = 40.328333333333333
quantile(dist4, static_cast<RealType>(0.5)), // 39.332839138842637
tolerance);
// PDF
BOOST_CHECK_CLOSE(
pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
static_cast<RealType>(0)),
static_cast<RealType>(1.831563888873410E-002), // probability.
tolerance);
BOOST_CHECK_CLOSE(
pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
static_cast<RealType>(2)),
static_cast<RealType>(1.465251111098740E-001), // probability.
tolerance);
BOOST_CHECK_CLOSE(
pdf(poisson_distribution<RealType>(static_cast<RealType>(20)), // mean big.
static_cast<RealType>(1)), // k small
static_cast<RealType>(4.122307244877130E-008), // probability.
tolerance);
BOOST_CHECK_CLOSE(
pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
static_cast<RealType>(20)), // K>> mean
static_cast<RealType>(8.277463646553730E-009), // probability.
tolerance);
// CDF
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(0)), // zero k events.
static_cast<RealType>(3.678794411714420E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(1)), // one k event.
static_cast<RealType>(7.357588823428830E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(2)), // two k events.
static_cast<RealType>(9.196986029286060E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(10)), // two k events.
static_cast<RealType>(9.999999899522340E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(15)), // two k events.
static_cast<RealType>(9.999999999999810E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(16)), // two k events.
static_cast<RealType>(9.999999999999990E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(17)), // two k events.
static_cast<RealType>(1.), // probability unity for double.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(33)), // k events at limit for float unchecked_factorial table.
static_cast<RealType>(1.), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(100)), // mean 100.
static_cast<RealType>(33)), // k events at limit for float unchecked_factorial table.
static_cast<RealType>(6.328271240363390E-15), // probability is tiny.
tolerance * static_cast<RealType>(2e11)); // 6.3495253382825722e-015 MathCAD
// Note that there two tiny probability are much more different.
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(100)), // mean 100.
static_cast<RealType>(34)), // k events at limit for float unchecked_factorial table.
static_cast<RealType>(1.898481372109020E-14), // probability is tiny.
tolerance*static_cast<RealType>(2e11)); // 1.8984813721090199e-014 MathCAD
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(33)), // mean = k
static_cast<RealType>(33)), // k events above limit for float unchecked_factorial table.
static_cast<RealType>(5.461191812386560E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(33)), // mean = k-1
static_cast<RealType>(34)), // k events above limit for float unchecked_factorial table.
static_cast<RealType>(6.133535681502950E-1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
static_cast<RealType>(34)), // k events above limit for float unchecked_factorial table.
static_cast<RealType>(1.), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
static_cast<RealType>(5)), // k events.
static_cast<RealType>(0.615960654833065), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
static_cast<RealType>(1)), // k events.
static_cast<RealType>(0.040427681994512805), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
static_cast<RealType>(0)), // k events (uses special case formula, not gamma).
static_cast<RealType>(0.006737946999085467), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(1.)), // mean
static_cast<RealType>(0)), // k events (uses special case formula, not gamma).
static_cast<RealType>(0.36787944117144233), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
static_cast<RealType>(10)), // k events.
static_cast<RealType>(0.5830397501929856), // probability.
tolerance);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
static_cast<RealType>(5)), // k events.
static_cast<RealType>(0.785130387030406), // probability.
tolerance);
// complement CDF
BOOST_CHECK_CLOSE( // Complement CDF
cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
static_cast<RealType>(5))), // k events.
static_cast<RealType>(1 - 0.785130387030406), // probability.
tolerance);
BOOST_CHECK_CLOSE( // Complement CDF
cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
static_cast<RealType>(0))), // Zero k events (uses special case formula, not gamma).
static_cast<RealType>(0.98168436111126578), // probability.
tolerance);
BOOST_CHECK_CLOSE( // Complement CDF
cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(1.)), // mean
static_cast<RealType>(0))), // Zero k events (uses special case formula, not gamma).
static_cast<RealType>(0.63212055882855767), // probability.
tolerance);
// Example where k is bigger than max_factorial (>34 for float)
// (therefore using log gamma so perhaps less accurate).
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(40.)), // mean
static_cast<RealType>(40)), // k events.
static_cast<RealType>(0.5419181783625430), // probability.
tolerance);
// Quantile & complement.
BOOST_CHECK_CLOSE(
boost::math::quantile(
poisson_distribution<RealType>(5), // mean.
static_cast<RealType>(0.615960654833065)), // probability.
static_cast<RealType>(5.), // Expect k = 5
tolerance/5); //
// EQUAL is too optimistic - fails [5.0000000000000124 != 5]
// BOOST_CHECK_EQUAL(boost::math::quantile( //
// poisson_distribution<RealType>(5.), // mean.
// static_cast<RealType>(0.615960654833065)), // probability.
// static_cast<RealType>(5.)); // Expect k = 5 events.
BOOST_CHECK_CLOSE(boost::math::quantile(
poisson_distribution<RealType>(4), // mean.
static_cast<RealType>(0.785130387030406)), // probability.
static_cast<RealType>(5.), // Expect k = 5 events.
tolerance/5);
// Check on quantile of other examples of inverse of cdf.
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
static_cast<RealType>(10)), // k events.
static_cast<RealType>(0.5830397501929856), // probability.
tolerance);
BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
poisson_distribution<RealType>(10.), // mean.
static_cast<RealType>(0.5830397501929856)), // probability.
static_cast<RealType>(10.), // Expect k = 10 events.
tolerance/5);
BOOST_CHECK_CLOSE(
cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
static_cast<RealType>(5)), // k events.
static_cast<RealType>(0.785130387030406), // probability.
tolerance);
BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
poisson_distribution<RealType>(4.), // mean.
static_cast<RealType>(0.785130387030406)), // probability.
static_cast<RealType>(5.), // Expect k = 10 events.
tolerance/5);
//BOOST_CHECK_CLOSE(boost::math::quantile(
// poisson_distribution<RealType>(5), // mean.
// static_cast<RealType>(0.785130387030406)), // probability.
// // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
// static_cast<RealType>(6.), // Expect k = 6 events.
// tolerance/5);
//BOOST_CHECK_CLOSE(boost::math::quantile(
// poisson_distribution<RealType>(5), // mean.
// static_cast<RealType>(0.77)), // probability.
// // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
// static_cast<RealType>(7.), // Expect k = 6 events.
// tolerance/5);
//BOOST_CHECK_CLOSE(boost::math::quantile(
// poisson_distribution<RealType>(5), // mean.
// static_cast<RealType>(0.75)), // probability.
// // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
// static_cast<RealType>(6.), // Expect k = 6 events.
// tolerance/5);
BOOST_CHECK_CLOSE(
boost::math::quantile(
complement(
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).
BOOST_CHECK_THROW(poisson mydudpoisson(-1), std::domain_error);// Mean must be > 0.
BOOST_CHECK_THROW(poisson mydudpoisson(-1), std::logic_error);// Mean must be > 0.
// Passes the check because logic_error is a parent????
// BOOST_CHECK_THROW(poisson mydudpoisson(-1), std::overflow_error); // fails the check
// because overflow_error is unrelated - except from std::exception
BOOST_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
*/