downsideSampleNumber_ (3) - Linux Manuals
downsideSampleNumber_: 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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