# cubicSum_ (3) - Linux Manuals

## cubicSum_: Statistics tool based on incremental accumulation.

## NAME

QuantLib::IncrementalStatistics - Statistics tool based on incremental accumulation.

## SYNOPSIS

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

### Public Types

### 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_**

## 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.

## Member Function Documentation

**Real** mean () const

returns the mean, defined as [

ngle = ac{um w_i x_i}{um w_i}. ]

**Real** variance () const

returns the variance, defined as [ ac{N}{N-1}

. ]

**Real** standardDeviation () const

returns the standard deviation $ igma $, 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{

}{igma^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{

}{igma^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{ um_{i=1}^{N} heta imes x_i^{2}}{ um_{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

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