{

// Median estimation of normal distribution N(1,1) using samples from a narrow normal distribution N(1,0.01)

// The weights equal to the likelihood ratio of the corresponding samples

// two random number generators

double mu = 1.;

double sigma_narrow = 0.01;

double sigma = 1.;

boost::lagged_fibonacci607 rng;

boost::normal_distribution<> mean_sigma_narrow(mu,sigma_narrow);

boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> > normal_narrow(rng, mean_sigma_narrow);

accumulator_set<double, stats<tag::weighted_median(with_p_square_quantile) >, double > acc;

accumulator_set<double, stats<tag::weighted_median(with_density) >, double >

acc_dens( density_cache_size = 10000, density_num_bins = 1000 );

accumulator_set<double, stats<tag::weighted_median(with_p_square_cumulative_distribution) >, double >

acc_cdist( p_square_cumulative_distribution_num_cells = 100 );

for (std::size_t i=0; i<1000000; ++i)

{

double sample = normal_narrow();

double w = std::exp(

0.5 * (sample - mu) * (sample - mu) * (

1./sigma_narrow/sigma_narrow - 1./sigma/sigma

)

);

acc(sample, weight = w);

acc_dens(sample, weight = w);

acc_cdist(sample, weight = w);

}

BOOST_CHECK_CLOSE(1., weighted_median(acc), 2);

BOOST_CHECK_CLOSE(1., weighted_median(acc_dens), 3);

BOOST_CHECK_CLOSE(1., weighted_median(acc_cdist), 3);