IncrementalStatistics Class Reference

Statistics tool based on incremental accumulation. More...

#include <incrementalstatistics.hpp>

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Public Types
typedef Real	value_type

Public Member Functions
	IncrementalStatistics ()
Inspectors
Size	samples () const
	number of samples collected More...
Real	weightSum () const
	sum of data weights More...
Real	mean () const
Real	variance () const
Real	standardDeviation () const
Real	errorEstimate () const
Real	skewness () const
Real	kurtosis () const
Real	min () const
Real	max () const
Size	downsideSamples () const
	number of negative samples collected More...
Real	downsideWeightSum () const
	sum of data weights for negative samples More...
Real	downsideVariance () const
Real	downsideDeviation () const

Modifiers
typedef boost::accumulators::accumulator_set< Real, boost::accumulators::stats< boost::accumulators::tag::count, boost::accumulators::tag::min, boost::accumulators::tag::max, boost::accumulators::tag::weighted_mean, boost::accumulators::tag::weighted_variance, boost::accumulators::tag::weighted_skewness, boost::accumulators::tag::weighted_kurtosis, boost::accumulators::tag::sum_of_weights >, Real >	accumulator_set
typedef boost::accumulators::accumulator_set< Real, boost::accumulators::stats< boost::accumulators::tag::count, boost::accumulators::tag::weighted_moment< 2 >, boost::accumulators::tag::sum_of_weights >, Real >	downside_accumulator_set
accumulator_set	acc_
downside_accumulator_set	downsideAcc_
void	add (Real value, Real weight=1.0)
	adds a datum to the set, possibly with a weight More...
template<class DataIterator >
void	addSequence (DataIterator begin, DataIterator end)
	adds a sequence of data to the set, with default weight More...
template<class DataIterator , class WeightIterator >
void	addSequence (DataIterator begin, DataIterator end, WeightIterator wbegin)
	adds a sequence of data to the set, each with its weight More...
void	reset ()
	resets the data to a null set More...

Detailed Description

Statistics tool based on incremental accumulation.

It can accumulate a set of data and return statistics (e.g: mean, variance, skewness, kurtosis, error estimation, etc.). This class is a wrapper to the boost accumulator library.

Definition at line 53 of file incrementalstatistics.hpp.

Member Typedef Documentation

value_type

typedef Real value_type

Definition at line 55 of file incrementalstatistics.hpp.

accumulator_set

typedef boost::accumulators::accumulator_set< Real, boost::accumulators::stats< boost::accumulators::tag::count, boost::accumulators::tag::min, boost::accumulators::tag::max, boost::accumulators::tag::weighted_mean, boost::accumulators::tag::weighted_variance, boost::accumulators::tag::weighted_skewness, boost::accumulators::tag::weighted_kurtosis, boost::accumulators::tag::sum_of_weights>, Real> accumulator_set

private

Definition at line 162 of file incrementalstatistics.hpp.

downside_accumulator_set

typedef boost::accumulators::accumulator_set< Real, boost::accumulators::stats< boost::accumulators::tag::count, boost::accumulators::tag::weighted_moment<2>, boost::accumulators::tag::sum_of_weights>, Real> downside_accumulator_set

private

Definition at line 169 of file incrementalstatistics.hpp.

Constructor & Destructor Documentation

IncrementalStatistics()

IncrementalStatistics

(

)

Definition at line 27 of file incrementalstatistics.cpp.

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Member Function Documentation

samples()

Size samples

(

)

const

number of samples collected

Definition at line 31 of file incrementalstatistics.cpp.

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weightSum()

Real weightSum

(

)

const

sum of data weights

Definition at line 36 of file incrementalstatistics.cpp.

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mean()

Real mean

(

)

const

returns the mean, defined as

$$\langle x \rangle = \frac{\sum w_i x_i}{\sum w_i}.$$

Definition at line 41 of file incrementalstatistics.cpp.

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variance()

Real variance

(

)

const

returns the variance, defined as

$$\frac{N}{N-1} \left\langle \left( x-\langle x \rangle \right)^2 \right\rangle.$$

Definition at line 47 of file incrementalstatistics.cpp.

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standardDeviation()

Real standardDeviation

(

)

const

returns the standard deviation $\sigma$, defined as the square root of the variance.

Definition at line 56 of file incrementalstatistics.cpp.

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errorEstimate()

Real errorEstimate

(

)

const

returns the error estimate $\epsilon$, defined as the square root of the ratio of the variance to the number of samples.

Definition at line 60 of file incrementalstatistics.cpp.

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skewness()

Real skewness

(

)

const

returns the skewness, defined as

$$\frac{N^2}{(N-1)(N-2)} \frac{\left\langle \left( x-\langle x \rangle \right)^3 \right\rangle}{\sigma^3}.$$

The above evaluates to 0 for a Gaussian distribution.

Definition at line 64 of file incrementalstatistics.cpp.

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kurtosis()

Real kurtosis

(

)

const

returns the excess kurtosis, defined as

$$\frac{N^2(N+1)}{(N-1)(N-2)(N-3)} \frac{\left\langle \left(x-\langle x \rangle \right)^4 \right\rangle}{\sigma^4} - \frac{3(N-1)^2}{(N-2)(N-3)}.$$

The above evaluates to 0 for a Gaussian distribution.

Definition at line 74 of file incrementalstatistics.cpp.

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min()

Real min

(

)

const

returns the minimum sample value

Definition at line 90 of file incrementalstatistics.cpp.

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max()

Real max

(

)

const

returns the maximum sample value

Definition at line 96 of file incrementalstatistics.cpp.

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downsideSamples()

Size downsideSamples

(

)

const

number of negative samples collected

Definition at line 102 of file incrementalstatistics.cpp.

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downsideWeightSum()

Real downsideWeightSum

(

)

const

sum of data weights for negative samples

Definition at line 107 of file incrementalstatistics.cpp.

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downsideVariance()

Real downsideVariance

(

)

const

returns the downside variance, defined as

$$\frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i}$$

, where $\theta$ = 0 if x > 0 and $\theta$ =1 if x <0

Definition at line 112 of file incrementalstatistics.cpp.

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downsideDeviation()

Real downsideDeviation

(

)

const

returns the downside deviation, defined as the square root of the downside variance.

Definition at line 122 of file incrementalstatistics.cpp.

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add()

void add	(	Real	value,
		Real	weight = 1.0
	)

adds a datum to the set, possibly with a weight

Precondition

weight must be positive or null

Definition at line 126 of file incrementalstatistics.cpp.

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addSequence() [1/2]

void addSequence	(	DataIterator	begin,
		DataIterator	end
	)

adds a sequence of data to the set, with default weight

Definition at line 136 of file incrementalstatistics.hpp.

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addSequence() [2/2]

void addSequence	(	DataIterator	begin,
		DataIterator	end,
		WeightIterator	wbegin
	)

adds a sequence of data to the set, each with its weight

Precondition

weights must be positive or null

Definition at line 143 of file incrementalstatistics.hpp.

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reset()

void reset

(

)

resets the data to a null set

Definition at line 134 of file incrementalstatistics.cpp.

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Member Data Documentation

acc_

accumulator_set acc_

private

Definition at line 163 of file incrementalstatistics.hpp.

downsideAcc_

downside_accumulator_set downsideAcc_

private

Definition at line 170 of file incrementalstatistics.hpp.