QuantLib 0.3.6
User manual
Introduction to QuantLib
QuantLib components
Reference manual
IncrementalStatistics Class Reference
#include <ql/Math/incrementalstatistics.hpp>
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 Member Functions | |
Inspectors | |
| Size | samples () const |
| number of samples collected | |
| double | weightSum () const |
| sum of data weights | |
| double | mean () const |
| double | variance () const |
| double | standardDeviation () const |
| double | downsideVariance () const |
| double | downsideDeviation () const |
| double | errorEstimate () const |
| double | skewness () const |
| double | kurtosis () const |
| double | min () const |
| double | max () const |
Modifiers | |
| void | add (double value, double 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_ |
| double | sampleWeight_ |
| double | downsideSampleWeight_ |
| double | sum_ |
| double | quadraticSum_ |
| double | downsideQuadraticSum_ |
| double | cubicSum_ |
| double | fourthPowerSum_ |
| double | min_ |
| double | max_ |
Member Function Documentation
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returns the mean, defined as
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![\[ \langle x \rangle = \frac{\sum w_i x_i}{\sum w_i}. \]](form_164.png)
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returns the variance, defined as
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![\[ \frac{N}{N-1} \left\langle \left( x-\langle x \rangle \right)^2 \right\rangle. \]](form_175.png)
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returns the standard deviation |
, defined as the square root of the variance.
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returns the downside variance, defined as
, where |
![\[ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} \]](form_160.png)
= 0 if x > 0 and
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returns the downside deviation, defined as the square root of the downside variance. |
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returns the error estimate |
, defined as the square root of the ratio of the variance to the number of samples.
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returns the skewness, defined as
The above evaluates to 0 for a Gaussian distribution. |
![\[ \frac{N^2}{(N-1)(N-2)} \frac{\left\langle \left( x-\langle x \rangle \right)^3 \right\rangle}{\sigma^3}. \]](form_167.png)
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returns the excess kurtosis, defined as
The above evaluates to 0 for a Gaussian distribution. |
![\[ \frac{N^2(N+1)}{(N-1)(N-2)(N-3)} \frac{\left\langle \left(x-\langle x \rangle \right)^4 \right\rangle}{\sigma^4} - \frac{3(N-1)^2}{(N-2)(N-3)}. \]](form_168.png)
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returns the minimum sample value |
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returns the maximum sample value |
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adds a datum to the set, possibly with a weight
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adds a sequence of data to the set, each with its weight
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