...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/extended_p_square.hpp>template<typenameSample>structextended_p_square_impl {// typestypedefnumeric::functional::average< Sample, std::size_t >::result_type float_type;typedefstd::vector< float_type > array_type;typedefunspecifiedresult_type;// construct/copy/destructtemplate<typenameArgs> extended_p_square_impl(Argsconst&);// public member functionstemplate<typenameArgs>voidoperator()(Argsconst&) ; result_type result(dont_care)const; };

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 generalizess the algorithm of

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