The count feature is a simple counter that tracks the number of samples pushed into the accumulator set.

Header

#include <boost/accumulators/statistics/count.hpp>

Example

accumulator_set<int, features<tag::count> > acc;
acc(0);
acc(0);
acc(0);
assert(3 == count(acc));

See also

The covariance feature is an iterative Monte Carlo estimator for the covariance. It is specified as tag::covariance<variate-type, variate-tag>.

Header

#include <boost/accumulators/statistics/covariance.hpp>

Example

accumulator_set<double, stats<tag::covariance<double, tag::covariate1> > > acc;
acc(1., covariate1 = 2.);
acc(1., covariate1 = 4.);
acc(2., covariate1 = 3.);
acc(6., covariate1 = 1.);
assert(covariance(acc) == -1.75);

See also

The tag::density feature returns a histogram of the sample distribution. For more implementation details, see density_impl.

Header

#include <boost/accumulators/statistics/density.hpp>

See also

The error_of<mean> feature calculates the error of the mean feature. It is equal to sqrt(variance / (count - 1)).

Header

#include <boost/accumulators/statistics/error_of.hpp>
#include <boost/accumulators/statistics/error_of_mean.hpp>

Example

accumulator_set<double, stats<tag::error_of<tag::mean> > > acc;
acc(1.1);
acc(1.2);
acc(1.3);
assert(0.057735 == error_of<tag::mean>(acc));

See also

Multiple quantile estimation with the extended P^2 algorithm. For further details, see extended_p_square_impl.

Header

#include <boost/accumulators/statistics/extended_p_square.hpp>

Example

boost::array<double> probs = {0.001,0.01,0.1,0.25,0.5,0.75,0.9,0.99,0.999};
accumulator_set<double, stats<tag::extended_p_square> >
    acc(tag::extended_p_square::probabilities = probs);

boost::lagged_fibonacci607 rng; // a random number generator
for (int i=0; i<10000; ++i)
    acc(rng());

BOOST_CHECK_CLOSE(extended_p_square(acc)[0], probs[0], 25);
BOOST_CHECK_CLOSE(extended_p_square(acc)[1], probs[1], 10);
BOOST_CHECK_CLOSE(extended_p_square(acc)[2], probs[2], 5);

for (std::size_t i=3; i < probs.size(); ++i)
{
    BOOST_CHECK_CLOSE(extended_p_square(acc)[i], probs[i], 2);
}

See also

Quantile estimation using the extended P^2 algorithm for weighted and unweighted samples. By default, the calculation is linear and unweighted, but quadratic and weighted variants are also provided. For further implementation details, see extended_p_square_quantile_impl.

All the variants share the tag::quantile feature and can be extracted using the quantile() extractor.

Header

#include <boost/accumulators/statistics/extended_p_square_quantile.hpp>

Example

typedef accumulator_set<double, stats<tag::extended_p_square_quantile> >
    accumulator_t;
typedef accumulator_set<double, stats<tag::weighted_extended_p_square_quantile>, double >
    accumulator_t_weighted;
typedef accumulator_set<double, stats<tag::extended_p_square_quantile(quadratic)> >
    accumulator_t_quadratic;
typedef accumulator_set<double, stats<tag::weighted_extended_p_square_quantile(quadratic)>, double >
    accumulator_t_weighted_quadratic;

// tolerance
double epsilon = 1;

// a random number generator
boost::lagged_fibonacci607 rng;

boost::array<double> probs = { 0.990, 0.991, 0.992, 0.993, 0.994, 
                               0.995, 0.996, 0.997, 0.998, 0.999 };
accumulator_t acc(extended_p_square_probabilities = probs);
accumulator_t_weighted acc_weighted(extended_p_square_probabilities = probs);
accumulator_t_quadratic acc2(extended_p_square_probabilities = probs);
accumulator_t_weighted_quadratic acc_weighted2(extended_p_square_probabilities = probs);

for (int i=0; i<10000; ++i)
{
    double sample = rng();
    acc(sample);
    acc2(sample);
    acc_weighted(sample, weight = 1.);
    acc_weighted2(sample, weight = 1.);
}

for (std::size_t i = 0; i < probs.size() - 1; ++i)
{
    BOOST_CHECK_CLOSE(
        quantile(acc, quantile_probability = 0.99025 + i*0.001)
      , 0.99025 + i*0.001
      , epsilon
    );
    BOOST_CHECK_CLOSE(
        quantile(acc2, quantile_probability = 0.99025 + i*0.001)
      , 0.99025 + i*0.001
      , epsilon
    );
    BOOST_CHECK_CLOSE(
        quantile(acc_weighted, quantile_probability = 0.99025 + i*0.001)
      , 0.99025 + i*0.001
      , epsilon
    );
    BOOST_CHECK_CLOSE(
        quantile(acc_weighted2, quantile_probability = 0.99025 + i*0.001)
      , 0.99025 + i*0.001
      , epsilon
    );
}

See also

The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central moment (the variance) of the samples, minus 3. The term -3 is added in order to ensure that the normal distribution has zero kurtosis. For more implementation details, see kurtosis_impl

Header

#include <boost/accumulators/statistics/kurtosis.hpp>

Example

accumulator_set<int, stats<tag::kurtosis > > acc;
    
acc(2);
acc(7);
acc(4);
acc(9);
acc(3);

BOOST_CHECK_EQUAL( mean(acc), 5 );
BOOST_CHECK_EQUAL( moment<2>(acc), 159./5. );
BOOST_CHECK_EQUAL( moment<3>(acc), 1171./5. );
BOOST_CHECK_EQUAL( moment<4>(acc), 1863 );
BOOST_CHECK_CLOSE( kurtosis(acc), -1.39965397924, 1e-6 );

See also

Calculates the maximum value of all the samples.

Header

#include <boost/accumulators/statistics/max.hpp>

Example

accumulator_set<int, stats<tag::max> > acc;

acc(1);
BOOST_CHECK_EQUAL(1, (max)(acc));

acc(0);
BOOST_CHECK_EQUAL(1, (max)(acc));

acc(2);
BOOST_CHECK_EQUAL(2, (max)(acc));

See also

Calculates the mean of samples, weights or variates. The calculation is either lazy (in the result extractor), or immediate (in the accumulator). The lazy implementation is the default. For more implementation details, see mean_impl or. immediate_mean_impl

Header

#include <boost/accumulators/statistics/mean.hpp>

Example

accumulator_set<
    int
  , stats<
        tag::mean
      , tag::mean_of_weights
      , tag::mean_of_variates<int, tag::covariate1>
    >
  , int 
> acc;

acc(1, weight = 2, covariate1 = 3);
BOOST_CHECK_CLOSE(1., mean(acc), 1e-5);
BOOST_CHECK_EQUAL(1u, count(acc));
BOOST_CHECK_EQUAL(2, sum(acc));
BOOST_CHECK_CLOSE(2., mean_of_weights(acc), 1e-5);
BOOST_CHECK_CLOSE(3., (mean_of_variates<int, tag::covariate1>(acc)), 1e-5);

acc(0, weight = 4, covariate1 = 4);
BOOST_CHECK_CLOSE(0.33333333333333333, mean(acc), 1e-5);
BOOST_CHECK_EQUAL(2u, count(acc));
BOOST_CHECK_EQUAL(2, sum(acc));
BOOST_CHECK_CLOSE(3., mean_of_weights(acc), 1e-5);
BOOST_CHECK_CLOSE(3.5, (mean_of_variates<int, tag::covariate1>(acc)), 1e-5);

acc(2, weight = 9, covariate1 = 8);
BOOST_CHECK_CLOSE(1.33333333333333333, mean(acc), 1e-5);
BOOST_CHECK_EQUAL(3u, count(acc));
BOOST_CHECK_EQUAL(20, sum(acc));
BOOST_CHECK_CLOSE(5., mean_of_weights(acc), 1e-5);
BOOST_CHECK_CLOSE(5., (mean_of_variates<int, tag::covariate1>(acc)), 1e-5);

accumulator_set<
    int
  , stats<
        tag::mean(immediate)
      , tag::mean_of_weights(immediate)
      , tag::mean_of_variates<int, tag::covariate1>(immediate)
    >
  , int
> acc2;

acc2(1, weight = 2, covariate1 = 3);
BOOST_CHECK_CLOSE(1., mean(acc2), 1e-5);
BOOST_CHECK_EQUAL(1u, count(acc2));
BOOST_CHECK_CLOSE(2., mean_of_weights(acc2), 1e-5);
BOOST_CHECK_CLOSE(3., (mean_of_variates<int, tag::covariate1>(acc2)), 1e-5);
    
acc2(0, weight = 4, covariate1 = 4);
BOOST_CHECK_CLOSE(0.33333333333333333, mean(acc2), 1e-5);
BOOST_CHECK_EQUAL(2u, count(acc2));
BOOST_CHECK_CLOSE(3., mean_of_weights(acc2), 1e-5);
BOOST_CHECK_CLOSE(3.5, (mean_of_variates<int, tag::covariate1>(acc2)), 1e-5);

acc2(2, weight = 9, covariate1 = 8);
BOOST_CHECK_CLOSE(1.33333333333333333, mean(acc2), 1e-5);
BOOST_CHECK_EQUAL(3u, count(acc2));
BOOST_CHECK_CLOSE(5., mean_of_weights(acc2), 1e-5);
BOOST_CHECK_CLOSE(5., (mean_of_variates<int, tag::covariate1>(acc2)), 1e-5);

See also

Median estimation based on the P^2 quantile estimator, the density estimator, or the P^2 cumulative distribution estimator. For more implementation details, see median_impl, with_density_median_impl, and with_p_square_cumulative_distribution_median_impl.

The three median accumulators all satisfy the tag::median feature, and can all be extracted with the median() extractor.

Header

#include <boost/accumulators/statistics/median.hpp>

Example

// two random number generators
double mu = 1.;
boost::lagged_fibonacci607 rng;
boost::normal_distribution<> mean_sigma(mu,1);
boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> >
    normal(rng, mean_sigma);

accumulator_set<double, stats<tag::median(with_p_square_quantile) > > acc;
accumulator_set<double, stats<tag::median(with_density) > > 
    acc_dens( density_cache_size = 10000, density_num_bins = 1000 );
accumulator_set<double, stats<tag::median(with_p_square_cumulative_distribution) > > 
    acc_cdist( p_square_cumulative_distribution_num_cells = 100 );
    
for (std::size_t i=0; i<100000; ++i)
{
    double sample = normal();
    acc(sample);
    acc_dens(sample);
    acc_cdist(sample);
}

BOOST_CHECK_CLOSE(1., median(acc), 1.);
BOOST_CHECK_CLOSE(1., median(acc_dens), 1.);
BOOST_CHECK_CLOSE(1., median(acc_cdist), 3.);

See also

Calculates the minimum value of all the samples.

Header

#include <boost/accumulators/statistics/min.hpp>

Example

accumulator_set<int, stats<tag::min> > acc;

acc(1);
BOOST_CHECK_EQUAL(1, (min)(acc));

acc(0);
BOOST_CHECK_EQUAL(0, (min)(acc));

acc(2);
BOOST_CHECK_EQUAL(0, (min)(acc));

See also

Calculates the N-th moment of the samples, which is defined as the sum of the N-th power of the samples over the count of samples.

Header

#include <boost/accumulators/statistics/moment.hpp>

Example

accumulator_set<int, stats<tag::moment<2> > > acc1;

acc1(2); //    4
acc1(4); //   16
acc1(5); // + 25
         // = 45 / 3 = 15

BOOST_CHECK_CLOSE(15., moment<2>(acc1), 1e-5);

accumulator_set<int, stats<tag::moment<5> > > acc2;

acc2(2); //     32
acc2(3); //    243
acc2(4); //   1024
acc2(5); // + 3125
         // = 4424 / 4 = 1106

BOOST_CHECK_CLOSE(1106., moment<5>(acc2), 1e-5);

See also

Histogram calculation of the cumulative distribution with the P^2 algorithm. For more implementation details, see p_square_cumulative_distribution_impl

Header

#include <boost/accumulators/statistics/p_square_cumulative_distribution.hpp>

Example

// tolerance in %
double epsilon = 3;

typedef accumulator_set<double, stats<tag::p_square_cumulative_distribution> > accumulator_t;
    
accumulator_t acc(tag::p_square_cumulative_distribution::num_cells = 100);

// two random number generators
boost::lagged_fibonacci607 rng;
boost::normal_distribution<> mean_sigma(0,1);
boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> > normal(rng, mean_sigma);

for (std::size_t i=0; i<100000; ++i)
{
    acc(normal());
}

typedef iterator_range<std::vector<std::pair<double, double> >::iterator > histogram_type;
histogram_type histogram = p_square_cumulative_distribution(acc);

for (std::size_t i = 0; i < histogram.size(); ++i)
{   
    // problem with small results: epsilon is relative (in percent), not absolute!
    if ( histogram[i].second > 0.001 )    
        BOOST_CHECK_CLOSE( 0.5 * (1.0 + erf( histogram[i].first / sqrt(2.0) )), histogram[i].second, epsilon );
}        

See also

Single quantile estimation with the P^2 algorithm. For more implementation details, see p_square_quantile_impl

Header

#include <boost/accumulators/statistics/p_square_quantile.hpp>

Example

typedef accumulator_set<double, stats<tag::p_square_quantile