Multiple quantile estimation with the extended $P^2$ algorithm. More...

#include <statistics_fwd.hpp>

Inheritance diagram for boost::accumulators::impl::extended_p_square_impl< Sample >:

Collaboration diagram for boost::accumulators::impl::extended_p_square_impl< Sample >:

Public Types
typedef numeric::functional::fdiv < Sample, std::size_t > ::result_type	float_type

typedef std::vector< float_type >	array_type

typedef iterator_range < detail::lvalue_index_iterator < permutation_iterator < typename array_type::const_iterator, detail::times2_iterator > > >	result_type

typedef mpl::false_	is_droppable

Public Member Functions
template<typename Args >
	extended_p_square_impl (Args const &args)

template<typename Args >
void	operator() (Args const &args)

result_type	result (dont_care) const

detail::void_	operator() (dont_care)

detail::void_	add_ref (dont_care)

detail::void_	drop (dont_care)

detail::void_	on_drop (dont_care)

Detailed Description

template<typename Sample>
struct boost::accumulators::impl::extended_p_square_impl< Sample >

Multiple quantile estimation with the extended $P^2$ algorithm.

Extended $P^2$ algorithm for estimation of several quantiles without storing samples. Assume that $m$ quantiles $\xi_{p_1}, \ldots, \xi_{p_m}$ are to be estimated. Instead of storing the whole sample cumulative distribution, the algorithm maintains only $m+2$ principal markers and $m+1$ 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 $ P^2 $ algorithm generalizes the $ P^2 $ 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.

Parameters

extended_p_square_probabilities A vector of quantile probabilities.