# QuantLib_IncrementalStatistics man page

IncrementalStatistics — Statistics tool based on incremental accumulation.

## Synopsis

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

### 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
Size downsideSamples () const
number of negative samples collected
Real downsideWeightSum () const
sum of data weights for negative samples
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

## 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.

## Member Function Documentation

### Real mean () const

returns the mean, defined as [ langle x rangle = ac{sum w_i x_i}{sum w_i}. ]

### Real variance () const

returns the variance, defined as [ ac{N}{N-1} leftlangle left( x-langle x rangle right)^2 rightrangle. ]

### Real standardDeviation () const

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

### Real errorEstimate () const

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

### Real skewness () const

returns the skewness, defined as [ ac{N^2}{(N-1)(N-2)} ac{leftlangle left( x-langle x rangle right)^3 rightrangle}{sigma^3}. ] The above evaluates to 0 for a Gaussian distribution.

### Real kurtosis () const

returns the excess kurtosis, defined as [ ac{N^2(N+1)}{(N-1)(N-2)(N-3)} ac{leftlangle left(x-langle x rangle right)^4 rightrangle}{sigma^4} - ac{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 [ ac{N}{N-1} imes ac{ sum_{i=1}^{N} heta imes x_i^{2}}{ sum_{i=1}^{N} w_i} ], where \$ heta \$ = 0 if x > 0 and \$ heta \$ =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

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

The man pages downsideSamples(3) and downsideWeightSum(3) are aliases of QuantLib_IncrementalStatistics(3).

Mon Apr 30 2018 Version 1.12.1 QuantLib