...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

boost::accumulators::impl::extended_p_square_impl — Multiple quantile estimation with the extended algorithm.

// In header: <boost/accumulators/statistics_fwd.hpp> template<typename Sample> struct extended_p_square_impl : public accumulator_base { // construct/copy/destruct template<typename Args> extended_p_square_impl(Args const &); // public member functions template<typename Args> void operator()(Args const &); result_type result(dont_care) const; template<typename Archive> void serialize(Archive &, const unsigned int); };

Extended algorithm for estimation of several quantiles without storing samples. Assume that quantiles are to be estimated. Instead of storing the whole sample cumulative distribution, the algorithm maintains only principal markers and middle markers, whose positions are updated with each sample and whose heights are adjusted (if necessary) using a piecewise-parablic formula. The heights of these central markers are the current estimates of the quantiles and returned as an iterator range.

For further details, see

K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49, Number 4 (October), 1986, p. 159-164.

The extended algorithm generalizes the algorithm of

R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and histograms without storing observations, Communications of the ACM, Volume 28 (October), Number 10, 1985, p. 1076-1085.