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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_general_statistics.html">GeneralStatistics</a></div>
<h1>GeneralStatistics Class Reference</h1><!-- doxytag: class="QuantLib::GeneralStatistics" --><code>#include <ql/math/statistics/generalstatistics.hpp></code>
<p>
<p>
<a href="class_quant_lib_1_1_general_statistics-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Statistics tool.
<p>
This class accumulates a set of data and returns their statistics (e.g: mean, variance, skewness, kurtosis, error estimation, percentile, etc.) based on the empirical distribution (no gaussian assumption)<p>
It doesn't suffer the numerical instability problem of <a class="el" href="class_quant_lib_1_1_incremental_statistics.html" title="Statistics tool based on incremental accumulation.">IncrementalStatistics</a>. The downside is that it stores all samples, thus increasing the memory requirements. <table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="64a1ba313ad4c1fd58bf5887c366df5a"></a><!-- doxytag: member="QuantLib::GeneralStatistics::value_type" ref="64a1ba313ad4c1fd58bf5887c366df5a" args="" -->
typedef <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>value_type</b></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">Inspectors</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="fb02dc74860bcd8ad0982324d50c82e4"></a><!-- doxytag: member="QuantLib::GeneralStatistics::samples" ref="fb02dc74860bcd8ad0982324d50c82e4" args="() const " -->
<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#fb02dc74860bcd8ad0982324d50c82e4">samples</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">number of samples collected <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="629a0510086a52a9a80da6f1bf8cb987"></a><!-- doxytag: member="QuantLib::GeneralStatistics::data" ref="629a0510086a52a9a80da6f1bf8cb987" args="() const " -->
const std::vector< std::pair<br>
< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> > > & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#629a0510086a52a9a80da6f1bf8cb987">data</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">collected data <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dadbb304259580be7add0941c9540bd9"></a><!-- doxytag: member="QuantLib::GeneralStatistics::weightSum" ref="dadbb304259580be7add0941c9540bd9" args="() const " -->
<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#dadbb304259580be7add0941c9540bd9">weightSum</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">sum of data weights <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#962ffe5a3593be370d5c883365c060f4">mean</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#4b8b05b2a9af92dad9cc304c2925a4eb">variance</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#f728e0bfb80c48d44424d590cbfda34e">standardDeviation</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#cc5ad105e834e2360818b4f5046bd1f5">errorEstimate</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#27cb1a211374553eadd4a0e09d60cf0c">skewness</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#8a4ed1d1339aae2ccc6bd69c8f026f10">kurtosis</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#c98e9ad7b67758707ccda2475bb90019">min</a> () const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#d849b4ad24b7c5b71e7ec46a65d53e8e">max</a> () const </td></tr>
<tr><td class="memTemplParams" nowrap colspan="2">template<class Func, class Predicate> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">std::pair< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>, <a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#4a787529df2476b6f6943dd57eb9fecc">expectationValue</a> (const Func &f, const Predicate &inRange) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#d85e1d17aa1273cc6b198d9109ef5c41">percentile</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> y) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#41d2156c2a2c3580b5ba66056b504a06">topPercentile</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> y) const </td></tr>
<tr><td colspan="2"><div class="groupHeader">Modifiers</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#3a1d26bb85ab23c2a935d09081c946fd">add</a> (<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> value, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> weight=1.0)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">adds a datum to the set, possibly with a weight <a href="#3a1d26bb85ab23c2a935d09081c946fd"></a><br></td></tr>
<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="3198ad07b15eca00872ebb3f6582ab98"></a><!-- doxytag: member="QuantLib::GeneralStatistics::addSequence" ref="3198ad07b15eca00872ebb3f6582ab98" args="(DataIterator begin, DataIterator end)" -->
template<class DataIterator> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#3198ad07b15eca00872ebb3f6582ab98">addSequence</a> (DataIterator begin, DataIterator end)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">adds a sequence of data to the set, with default weight <br></td></tr>
<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="a738e0347128708ce547e4df6eb3d1cc"></a><!-- doxytag: member="QuantLib::GeneralStatistics::addSequence" ref="a738e0347128708ce547e4df6eb3d1cc" args="(DataIterator begin, DataIterator end, WeightIterator wbegin)" -->
template<class DataIterator, class WeightIterator> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#a738e0347128708ce547e4df6eb3d1cc">addSequence</a> (DataIterator begin, DataIterator end, WeightIterator wbegin)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">adds a sequence of data to the set, each with its weight <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d20897c5c8bd47f5d4005989bead0e55"></a><!-- doxytag: member="QuantLib::GeneralStatistics::reset" ref="d20897c5c8bd47f5d4005989bead0e55" args="()" -->
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#d20897c5c8bd47f5d4005989bead0e55">reset</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">resets the data to a null set <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="10ee1a10d90af08c04aff52692a5747e"></a><!-- doxytag: member="QuantLib::GeneralStatistics::sort" ref="10ee1a10d90af08c04aff52692a5747e" args="() const " -->
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_general_statistics.html#10ee1a10d90af08c04aff52692a5747e">sort</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">sort the data set in increasing order <br></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="962ffe5a3593be370d5c883365c060f4"></a><!-- doxytag: member="QuantLib::GeneralStatistics::mean" ref="962ffe5a3593be370d5c883365c060f4" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> mean </td>
<td>(</td>
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<td width="100%"> const</td>
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returns the mean, defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \langle x \rangle = \frac{\sum w_i x_i}{\sum w_i}. \]" src="form_185.png">
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<a class="anchor" name="4b8b05b2a9af92dad9cc304c2925a4eb"></a><!-- doxytag: member="QuantLib::GeneralStatistics::variance" ref="4b8b05b2a9af92dad9cc304c2925a4eb" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> variance </td>
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returns the variance, defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \sigma^2 = \frac{N}{N-1} \left\langle \left( x-\langle x \rangle \right)^2 \right\rangle. \]" src="form_186.png">
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<a class="anchor" name="f728e0bfb80c48d44424d590cbfda34e"></a><!-- doxytag: member="QuantLib::GeneralStatistics::standardDeviation" ref="f728e0bfb80c48d44424d590cbfda34e" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> standardDeviation </td>
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returns the standard deviation <img class="formulaInl" alt="$ \sigma $" src="form_4.png">, defined as the square root of the variance.
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<a class="anchor" name="cc5ad105e834e2360818b4f5046bd1f5"></a><!-- doxytag: member="QuantLib::GeneralStatistics::errorEstimate" ref="cc5ad105e834e2360818b4f5046bd1f5" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> errorEstimate </td>
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returns the error estimate on the mean value, defined as <img class="formulaInl" alt="$ \epsilon = \sigma/\sqrt{N}. $" src="form_187.png">
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<a class="anchor" name="27cb1a211374553eadd4a0e09d60cf0c"></a><!-- doxytag: member="QuantLib::GeneralStatistics::skewness" ref="27cb1a211374553eadd4a0e09d60cf0c" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> skewness </td>
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returns the skewness, defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{N^2}{(N-1)(N-2)} \frac{\left\langle \left( x-\langle x \rangle \right)^3 \right\rangle}{\sigma^3}. \]" src="form_188.png">
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The above evaluates to 0 for a Gaussian distribution.
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<a class="anchor" name="8a4ed1d1339aae2ccc6bd69c8f026f10"></a><!-- doxytag: member="QuantLib::GeneralStatistics::kurtosis" ref="8a4ed1d1339aae2ccc6bd69c8f026f10" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> kurtosis </td>
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<td width="100%"> const</td>
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returns the excess kurtosis, defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{N^2(N+1)}{(N-1)(N-2)(N-3)} \frac{\left\langle \left(x-\langle x \rangle \right)^4 \right\rangle}{\sigma^4} - \frac{3(N-1)^2}{(N-2)(N-3)}. \]" src="form_189.png">
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The above evaluates to 0 for a Gaussian distribution.
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<a class="anchor" name="c98e9ad7b67758707ccda2475bb90019"></a><!-- doxytag: member="QuantLib::GeneralStatistics::min" ref="c98e9ad7b67758707ccda2475bb90019" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> min </td>
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returns the minimum sample value
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<a class="anchor" name="d849b4ad24b7c5b71e7ec46a65d53e8e"></a><!-- doxytag: member="QuantLib::GeneralStatistics::max" ref="d849b4ad24b7c5b71e7ec46a65d53e8e" args="() const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> max </td>
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returns the maximum sample value
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<a class="anchor" name="4a787529df2476b6f6943dd57eb9fecc"></a><!-- doxytag: member="QuantLib::GeneralStatistics::expectationValue" ref="4a787529df2476b6f6943dd57eb9fecc" args="(const Func &f, const Predicate &inRange) const " -->
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<td class="memname">std::pair<<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>,<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a>> expectationValue </td>
<td>(</td>
<td class="paramtype">const Func & </td>
<td class="paramname"> <em>f</em>, </td>
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<td class="paramname"> <em>inRange</em></td><td> </td>
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Expectation value of a function <img class="formulaInl" alt="$ f $" src="form_41.png"> on a given range <img class="formulaInl" alt="$ \mathcal{R} $" src="form_190.png">, i.e., <p class="formulaDsp">
<img class="formulaDsp" alt="\[ \mathrm{E}\left[f \;|\; \mathcal{R}\right] = \frac{\sum_{x_i \in \mathcal{R}} f(x_i) w_i}{ \sum_{x_i \in \mathcal{R}} w_i}. \]" src="form_191.png">
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The range is passed as a boolean function returning <code>true</code> if the argument belongs to the range or <code>false</code> otherwise.<p>
The function returns a pair made of the result and the number of observations in the given range.
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<a class="anchor" name="d85e1d17aa1273cc6b198d9109ef5c41"></a><!-- doxytag: member="QuantLib::GeneralStatistics::percentile" ref="d85e1d17aa1273cc6b198d9109ef5c41" args="(Real y) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> percentile </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>y</em> </td>
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<img class="formulaInl" alt="$ y $" src="form_13.png">-th percentile, defined as the value <img class="formulaInl" alt="$ \bar{x} $" src="form_192.png"> such that <p class="formulaDsp">
<img class="formulaDsp" alt="\[ y = \frac{\sum_{x_i < \bar{x}} w_i}{ \sum_i w_i} \]" src="form_193.png">
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<dl class="pre" compact><dt><b>Precondition:</b></dt><dd><img class="formulaInl" alt="$ y $" src="form_13.png"> must be in the range <img class="formulaInl" alt="$ (0-1]. $" src="form_194.png"> </dd></dl>
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<a class="anchor" name="41d2156c2a2c3580b5ba66056b504a06"></a><!-- doxytag: member="QuantLib::GeneralStatistics::topPercentile" ref="41d2156c2a2c3580b5ba66056b504a06" args="(Real y) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> topPercentile </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>y</em> </td>
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<img class="formulaInl" alt="$ y $" src="form_13.png">-th top percentile, defined as the value <img class="formulaInl" alt="$ \bar{x} $" src="form_192.png"> such that <p class="formulaDsp">
<img class="formulaDsp" alt="\[ y = \frac{\sum_{x_i > \bar{x}} w_i}{ \sum_i w_i} \]" src="form_195.png">
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<dl class="pre" compact><dt><b>Precondition:</b></dt><dd><img class="formulaInl" alt="$ y $" src="form_13.png"> must be in the range <img class="formulaInl" alt="$ (0-1]. $" src="form_194.png"> </dd></dl>
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<a class="anchor" name="3a1d26bb85ab23c2a935d09081c946fd"></a><!-- doxytag: member="QuantLib::GeneralStatistics::add" ref="3a1d26bb85ab23c2a935d09081c946fd" args="(Real value, Real weight=1.0)" -->
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<td class="memname">void add </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>value</em>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>weight</em> = <code>1.0</code></td><td> </td>
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adds a datum to the set, possibly with a weight
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<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>weights must be positive or null </dd></dl>
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