GeneralStatistics Class Reference

Statistics tool. More...

#include <ql/math/statistics/generalstatistics.hpp>

Collaboration diagram for GeneralStatistics:

Public Types
typedef Real	value_type

Public Member Functions
	GeneralStatistics ()
Inspectors
Size	samples () const
	number of samples collected More...
const std::vector< std::pair< Real, Real > > &	data () const
	collected data 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
template<class Func , class Predicate >
std::pair< Real, Size >	expectationValue (const Func &f, const Predicate &inRange) const
template<class Func >
std::pair< Real, Size >	expectationValue (const Func &f) const
Real	percentile (Real y) const
Real	topPercentile (Real y) const

Modifiers
std::vector< std::pair< Real, Real > >	samples_
bool	sorted_
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...
void	reserve (Size n) const
	informs the internal storage of a planned increase in size More...
void	sort () const
	sort the data set in increasing order More...

Detailed Description

Statistics tool.

This class accumulates a set of data and returns their statistics (e.g: mean, variance, skewness, kurtosis, error estimation, percentile, etc.) based on the empirical distribution (no gaussian assumption)

It doesn't suffer the numerical instability problem of IncrementalStatistics. The downside is that it stores all samples, thus increasing the memory requirements.

Definition at line 46 of file generalstatistics.hpp.

Member Typedef Documentation

value_type

typedef Real value_type

Definition at line 48 of file generalstatistics.hpp.

Constructor & Destructor Documentation

GeneralStatistics()

GeneralStatistics

(

)

Definition at line 198 of file generalstatistics.hpp.

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Member Function Documentation

samples()

Size samples

(

)

const

number of samples collected

Definition at line 202 of file generalstatistics.hpp.

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data()

const std::vector< std::pair< Real, Real > > & data

(

)

const

collected data

Definition at line 207 of file generalstatistics.hpp.

weightSum()

Real weightSum

(

)

const

sum of data weights

Definition at line 25 of file generalstatistics.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 34 of file generalstatistics.cpp.

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variance()

Real variance

(

)

const

returns the variance, defined as

\[ \sigma^2 = \frac{N}{N-1} \left\langle \left( x-\langle x \rangle \right)^2 \right\rangle. \]

Definition at line 40 of file generalstatistics.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 211 of file generalstatistics.hpp.

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errorEstimate()

Real errorEstimate

(

)

const

returns the error estimate on the mean value, defined as \( \epsilon = \sigma/\sqrt{N}. \)

Definition at line 215 of file generalstatistics.hpp.

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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 54 of file generalstatistics.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 69 of file generalstatistics.cpp.

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min()

Real min

(

)

const

returns the minimum sample value

Definition at line 219 of file generalstatistics.hpp.

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max()

Real max

(

)

const

returns the maximum sample value

Definition at line 225 of file generalstatistics.hpp.

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expectationValue() [1/2]

std::pair< Real, Size > expectationValue	(	const Func &	f,
		const Predicate &	inRange
	)		const

Expectation value of a function \( f \) on a given range \( \mathcal{R} \), i.e.,

\[ \mathrm{E}\left[f \;|\; \mathcal{R}\right] = \frac{\sum_{x_i \in \mathcal{R}} f(x_i) w_i}{ \sum_{x_i \in \mathcal{R}} w_i}. \]

The range is passed as a boolean function returning true if the argument belongs to the range or false otherwise.

The function returns a pair made of the result and the number of observations in the given range.

Definition at line 116 of file generalstatistics.hpp.

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expectationValue() [2/2]

std::pair< Real, Size > expectationValue

(

const Func &

f

)

const

Expectation value of a function \( f \) over the whole set of samples; equivalent to passing the other overload a range function always returning true.

Definition at line 140 of file generalstatistics.hpp.

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percentile()

Real percentile

(

Real

y

)

const

\( y \)-th percentile, defined as the value \( \bar{x} \) such that

\[ y = \frac{\sum_{x_i < \bar{x}} w_i}{ \sum_i w_i} \]

Precondition

\( y \) must be in the range \( (0-1]. \)

Definition at line 88 of file generalstatistics.cpp.

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topPercentile()

Real topPercentile

(

Real

y

)

const

\( y \)-th top percentile, defined as the value \( \bar{x} \) such that

\[ y = \frac{\sum_{x_i > \bar{x}} w_i}{ \sum_i w_i} \]

Precondition

\( y \) must be in the range \( (0-1]. \)

Definition at line 112 of file generalstatistics.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

weights must be positive or null

Definition at line 232 of file generalstatistics.hpp.

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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 169 of file generalstatistics.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

Definition at line 175 of file generalstatistics.hpp.

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reset()

void reset

(

)

resets the data to a null set

Definition at line 238 of file generalstatistics.hpp.

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reserve()

void reserve

(

Size

n

)

const

informs the internal storage of a planned increase in size

Definition at line 243 of file generalstatistics.hpp.

sort()

void sort

(

)

const

sort the data set in increasing order

Definition at line 247 of file generalstatistics.hpp.

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Member Data Documentation

samples_

std::vector<std::pair<Real,Real> > samples_

mutableprivate

Definition at line 191 of file generalstatistics.hpp.

sorted_

bool sorted_

mutableprivate

Definition at line 192 of file generalstatistics.hpp.