IncrementalStatistics Class Reference

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

List of all members.


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.)

Warning:
high moments are numerically unstable for high average/standardDeviation ratios.


Public Types

typedef Real value_type

Public Member Functions

Inspectors
Size samples () const
 number of samples collected
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
Real downsideVariance () const
Real downsideDeviation () 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

Protected Attributes

Size sampleNumber_
Size downsideSampleNumber_
Real sampleWeight_
Real downsideSampleWeight_
Real sum_
Real quadraticSum_
Real downsideQuadraticSum_
Real cubicSum_
Real fourthPowerSum_
Real min_
Real max_


Member Function Documentation

Real mean (  )  const

returns the mean, defined as

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

Real variance (  )  const

returns the variance, defined as

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

Real standardDeviation (  )  const

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

Real errorEstimate (  )  const

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

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.

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.

Real min (  )  const

returns the minimum sample value

Real max (  )  const

returns the maximum sample value

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

Real downsideDeviation (  )  const

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

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

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