# downsideDeviation (3) - Linux Manuals

## NAME

QuantLib::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

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 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

Generated automatically by Doxygen for QuantLib from the source code.