Wed, 14 Dec 2016 16:38:43 GMT

Actually, looking again at Table I in the paper, there is the possibility that intermediate calculations were made with rounded figures, and that may explain explain the discrepancy. I need to verify my paper & pencil calculations again before I can say that conclusively.

-- Sinan

Wed, 14 Dec 2016 17:43:24 GMT

This is the final actually: As I was verifying intermediate calculations by hand, I noticed that the body of the paper lists the first five observations as

0.02, 0.5, 0.74, 3.99, 0.83

whereas they use

0.02, 0.15, 0.74, 3.99, 0.83

to produce Table I.

With that adjustment, the program:

#include <algorithm>
#include <cstdio>
#include <string>
#include <utility>
#include <vector>
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/stats.hpp>
#include <boost/accumulators/statistics/median.hpp>
namespace bacc = boost::accumulators;
int main(void)
{
    bacc::accumulator_set<double,
        bacc::stats<bacc::tag::median(bacc::with_p_square_quantile)> > acc;
    // See http://www.cse.wustl.edu/~jain/papers/psqr.htm
    // First five observations
    acc(0.02);
    acc(0.15);
    acc(0.74);
    acc(3.39);
    acc(0.83);
    const std::vector<std::pair<double, double> > jain_chlamtac {
        {22.37, 0.74},
        {10.15, 0.74},
        {15.43, 2.18},
        {38.62, 4.75},
        {15.92, 4.75},
        {34.60, 9.28},
        {10.28, 9.28},
        {1.47,  9.28},
        {0.40,  9.28},
        {0.05,  6.30},
        {11.39, 6.30},
        {0.27,  6.30},
        {0.42,  6.30},
        {0.09,  4.44},
        {11.37, 4.44},
    };
    for (auto p: jain_chlamtac)
    {
        acc(p.first);
        std::printf("calculated= %.3f\texpected= %.2f\n", bacc::median(acc), p.second);
    }
    return 0;
}

produces the output:

calculated= 0.740       expected= 0.74
calculated= 0.740       expected= 0.74
calculated= 2.178       expected= 2.18
calculated= 4.753       expected= 4.75
calculated= 4.753       expected= 4.75
calculated= 9.275       expected= 9.28
calculated= 9.275       expected= 9.28
calculated= 9.275       expected= 9.28
calculated= 9.275       expected= 9.28
calculated= 6.297       expected= 6.30
calculated= 6.297       expected= 6.30
calculated= 6.297       expected= 6.30
calculated= 6.297       expected= 6.30
calculated= 4.441       expected= 4.44
calculated= 4.441       expected= 4.44

which is definitely good enough.

I sent an email to Dr. Jain pointing out the discrepancy between the text of the paper and the numbers used to produce Table I.

This removes my concern that there was something subtly wrong with the implementation in p_square_quantile.hpp (I did re-write the key sections several times trying to figure out what it might be) and establishes that the implementation can replicate the output in the original paper.

I still think the test needs to be improved, but now I feel free to focus on that.

I will submit a pull request as soon as I have some time to put it together.

HTH,

-- Sinan

Boost C++ Libraries: Ticket #12688: Boost..Accumulators test/median.cpp testing method is flawed