GeneralStatistics Class Reference

Statistics tool. More...

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

Inheritance diagram for GeneralStatistics:

Public Types
typedef Real	value_type

Public Member Functions
Inspectors
Size	samples () const
	number of samples collected
const std::vector< std::pair< Real, Real > > &	data () const
	collected data
Real	weightSum () const
	sum of data weights
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
void	add (Real value, Real weight=1.0)
	adds a datum to the set, possibly with a weight
template<class DataIterator>
void	addSequence (DataIterator begin, DataIterator end)
	adds a sequence of data to the set, with default weight
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
void	reset ()
	resets the data to a null set
void	reserve (Size n) const
	informs the internal storage of a planned increase in size
void	sort () const
	sort the data set in increasing order

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.

Member Function Documentation

mean()

Real mean

(

)

const

returns the mean, defined as

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

Examples

MarketModels.cpp.

variance()

Real variance

(

)

const

returns the variance, defined as

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

standardDeviation()

Real standardDeviation

(

)

const

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

errorEstimate()

Real errorEstimate

(

)

const

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

Examples

MarketModels.cpp.

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.

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.

min()

Real min

(

)

const

returns the minimum sample value

max()

Real max

(

)

const

returns the maximum sample value

expectationValue() [1/2]

template<class Func, class Predicate>

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.

expectationValue() [2/2]

template<class Func>

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.

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 \( (0-1]. \)

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 \( (0-1]. \)

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