Math.NET Numerics
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<div class="header">
<p class="class"><strong>Type</strong> Statistics</p>
<p><strong>Namespace</strong> MathNet.Numerics.Statistics</p>
</div>
<div class="sub-header">
<div id="summary">Extension methods to return basic statistics on set of data.
</div>
<h3 class="section">Static Functions</h3>
<ul>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Covariance">Covariance</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#EmpiricalCDF">EmpiricalCDF</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#EmpiricalCDF">EmpiricalCDF</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#EmpiricalCDFFunc">EmpiricalCDFFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#EmpiricalInvCDF">EmpiricalInvCDF</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#EmpiricalInvCDFFunc">EmpiricalInvCDFFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Entropy">Entropy</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#FiveNumberSummary">FiveNumberSummary</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#GeometricMean">GeometricMean</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#HarmonicMean">HarmonicMean</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#InterquartileRange">InterquartileRange</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Kurtosis">Kurtosis</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#LowerQuartile">LowerQuartile</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Maximum">Maximum</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MaximumAbsolute">MaximumAbsolute</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MaximumMagnitudePhase">MaximumMagnitudePhase</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Mean">Mean</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MeanStandardDeviation">MeanStandardDeviation</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MeanVariance">MeanVariance</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Median">Median</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Minimum">Minimum</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MinimumAbsolute">MinimumAbsolute</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MinimumMagnitudePhase">MinimumMagnitudePhase</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#MovingAverage">MovingAverage</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#OrderStatistic">OrderStatistic</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#OrderStatisticFunc">OrderStatisticFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Percentile">Percentile</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PercentileFunc">PercentileFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PopulationCovariance">PopulationCovariance</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PopulationKurtosis">PopulationKurtosis</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PopulationSkewness">PopulationSkewness</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PopulationSkewnessKurtosis">PopulationSkewnessKurtosis</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PopulationStandardDeviation">PopulationStandardDeviation</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#PopulationVariance">PopulationVariance</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Quantile">Quantile</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#QuantileCustom">QuantileCustom</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#QuantileCustomFunc">QuantileCustomFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#QuantileFunc">QuantileFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#QuantileRank">QuantileRank</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#QuantileRank">QuantileRank</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#QuantileRankFunc">QuantileRankFunc</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Ranks">Ranks</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#RootMeanSquare">RootMeanSquare</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Skewness">Skewness</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#SkewnessKurtosis">SkewnessKurtosis</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#StandardDeviation">StandardDeviation</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#UpperQuartile">UpperQuartile</a></li>
<li><a href="../MathNet.Numerics.Statistics/Statistics.htm#Variance">Variance</a></li>
</ul>
</div>
<h3 class="section">Public Static Functions</h3>
<div id="Covariance" class="method">
<h4><span title="System.double">double</span> <strong>Covariance</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples1, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples2)</h4>
<div class="content">Estimates the unbiased population covariance from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN if data has less than two entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples1</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples2</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
</div>
</div>
</div>
<div id="EmpiricalCDF" class="method">
<h4><span title="System.double">double</span> <strong>EmpiricalCDF</strong>(this <span title="System.Collections.Generic.IEnumerable<float>">IEnumerable&lt;float&gt;</span> data, <span title="System.float">float</span> x)</h4>
<div class="content">Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<float>">IEnumerable&lt;float&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.float">float</span></code> x</h6>
<p class="comments">The value where to estimate the CDF at. </p>
</div>
</div>
</div>
<div id="EmpiricalCDF" class="method">
<h4><span title="System.double">double</span> <strong>EmpiricalCDF</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.double">double</span> x)</h4>
<div class="content">Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.double">double</span></code> x</h6>
<p class="comments">The value where to estimate the CDF at. </p>
</div>
</div>
</div>
<div id="EmpiricalCDFFunc" class="method">
<h4><span title="System.Func<double, double>">Func&lt;double, double&gt;</span> <strong>EmpiricalCDFFunc</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="EmpiricalInvCDF" class="method">
<h4><span title="System.double">double</span> <strong>EmpiricalInvCDF</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.double">double</span> tau)</h4>
<div class="content">Estimates the empirical inverse CDF at tau from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.double">double</span></code> tau</h6>
<p class="comments">Quantile selector, between 0.0 and 1.0 (inclusive). </p>
</div>
</div>
</div>
<div id="EmpiricalInvCDFFunc" class="method">
<h4><span title="System.Func<double, double>">Func&lt;double, double&gt;</span> <strong>EmpiricalInvCDFFunc</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the empirical inverse CDF at tau from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="Entropy" class="method">
<h4><span title="System.double">double</span> <strong>Entropy</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Calculates the entropy of a stream of double values in bits.
Returns NaN if any of the values in the stream are NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="FiveNumberSummary" class="method">
<h4><span title="System.Double[]">Double[]</span> <strong>FiveNumberSummary</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates {min, lower-quantile, median, upper-quantile, max} from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="GeometricMean" class="method">
<h4><span title="System.double">double</span> <strong>GeometricMean</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Evaluates the geometric mean.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data to calculate the geometric mean of. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The geometric mean of the sample. </p>
</div>
</div>
</div>
<div id="HarmonicMean" class="method">
<h4><span title="System.double">double</span> <strong>HarmonicMean</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Evaluates the harmonic mean.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data to calculate the harmonic mean of. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The harmonic mean of the sample. </p>
</div>
</div>
</div>
<div id="InterquartileRange" class="method">
<h4><span title="System.double">double</span> <strong>InterquartileRange</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the inter-quartile range from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="Kurtosis" class="method">
<h4><span title="System.double">double</span> <strong>Kurtosis</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the unbiased population kurtosis from the provided samples.
Uses a normalizer (Bessel's correction; type 2).
Returns NaN if data has less than four entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
</div>
</div>
</div>
<div id="LowerQuartile" class="method">
<h4><span title="System.double">double</span> <strong>LowerQuartile</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the first quartile value from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="Maximum" class="method">
<h4><span title="System.double">double</span> <strong>Maximum</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Returns the maximum value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The sample data. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The maximum value in the sample data. </p>
</div>
</div>
</div>
<div id="MaximumAbsolute" class="method">
<h4><span title="System.double">double</span> <strong>MaximumAbsolute</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Returns the maximum absolute value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The sample data. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The maximum value in the sample data. </p>
</div>
</div>
</div>
<div id="MaximumMagnitudePhase" class="method">
<h4><span title="System.Numerics.Complex">Complex</span> <strong>MaximumMagnitudePhase</strong>(this <span title="System.Collections.Generic.IEnumerable<Complex>">IEnumerable&lt;Complex&gt;</span> data)</h4>
<div class="content">Returns the maximum magnitude and phase value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<Complex>">IEnumerable&lt;Complex&gt;</span></code> data</h6>
<p class="comments">The sample data. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.Numerics.Complex">Complex</span></code></h6>
<p>The minimum value in the sample data. </p>
</div>
</div>
</div>
<div id="Mean" class="method">
<h4><span title="System.double">double</span> <strong>Mean</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Evaluates the sample mean, an estimate of the population mean.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data to calculate the mean of. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The mean of the sample. </p>
</div>
</div>
</div>
<div id="MeanStandardDeviation" class="method">
<h4><span title="System.ValueTuple<double, double>">ValueTuple&lt;double, double&gt;</span> <strong>MeanStandardDeviation</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the sample mean and the unbiased population standard deviation from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or if any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">The data to calculate the mean of. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.ValueTuple<double, double>">ValueTuple&lt;double, double&gt;</span></code></h6>
<p>The mean of the sample. </p>
</div>
</div>
</div>
<div id="MeanVariance" class="method">
<h4><span title="System.ValueTuple<double, double>">ValueTuple&lt;double, double&gt;</span> <strong>MeanVariance</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the sample mean and the unbiased population variance from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or if any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">The data to calculate the mean of. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.ValueTuple<double, double>">ValueTuple&lt;double, double&gt;</span></code></h6>
<p>The mean of the sample. </p>
</div>
</div>
</div>
<div id="Median" class="method">
<h4><span title="System.double">double</span> <strong>Median</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the sample median from the provided samples (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="Minimum" class="method">
<h4><span title="System.double">double</span> <strong>Minimum</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Returns the minimum value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The sample data. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The minimum value in the sample data. </p>
</div>
</div>
</div>
<div id="MinimumAbsolute" class="method">
<h4><span title="System.double">double</span> <strong>MinimumAbsolute</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Returns the minimum absolute value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The sample data. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.double">double</span></code></h6>
<p>The minimum value in the sample data. </p>
</div>
</div>
</div>
<div id="MinimumMagnitudePhase" class="method">
<h4><span title="System.Numerics.Complex">Complex</span> <strong>MinimumMagnitudePhase</strong>(this <span title="System.Collections.Generic.IEnumerable<Complex>">IEnumerable&lt;Complex&gt;</span> data)</h4>
<div class="content">Returns the minimum magnitude and phase value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<Complex>">IEnumerable&lt;Complex&gt;</span></code> data</h6>
<p class="comments">The sample data. </p>
</div>
<div class="return">
<h5>Return</h5>
<h6><code><span title="System.Numerics.Complex">Complex</span></code></h6>
<p>The minimum value in the sample data. </p>
</div>
</div>
</div>
<div id="MovingAverage" class="method">
<h4><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> <strong>MovingAverage</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples, <span title="System.int">int</span> windowSize)</h4>
<div class="content">Evaluates the sample mean over a moving window, for each samples.
Returns NaN if no data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">The sample stream to calculate the mean of. </p>
<h6><code><span title="System.int">int</span></code> windowSize</h6>
<p class="comments">The number of last samples to consider. </p>
</div>
</div>
</div>
<div id="OrderStatistic" class="method">
<h4><span title="System.double">double</span> <strong>OrderStatistic</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.int">int</span> order)</h4>
<div class="content">Returns the order statistic (order 1..N) from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.int">int</span></code> order</h6>
<p class="comments">One-based order of the statistic, must be between 1 and N (inclusive). </p>
</div>
</div>
</div>
<div id="OrderStatisticFunc" class="method">
<h4><span title="System.Func<int, double>">Func&lt;int, double&gt;</span> <strong>OrderStatisticFunc</strong>(<span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Returns the order statistic (order 1..N) from the provided samples.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="Percentile" class="method">
<h4><span title="System.double">double</span> <strong>Percentile</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.int">int</span> p)</h4>
<div class="content">Estimates the p-Percentile value from the provided samples.
If a non-integer Percentile is needed, use Quantile instead.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.int">int</span></code> p</h6>
<p class="comments">Percentile selector, between 0 and 100 (inclusive). </p>
</div>
</div>
</div>
<div id="PercentileFunc" class="method">
<h4><span title="System.Func<int, double>">Func&lt;int, double&gt;</span> <strong>PercentileFunc</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the p-Percentile value from the provided samples.
If a non-integer Percentile is needed, use Quantile instead.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="PopulationCovariance" class="method">
<h4><span title="System.double">double</span> <strong>PopulationCovariance</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population1, <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population2)</h4>
<div class="content">Evaluates the population covariance from the provided full populations.
On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population1</h6>
<p class="comments">The full population data. </p>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population2</h6>
<p class="comments">The full population data. </p>
</div>
</div>
</div>
<div id="PopulationKurtosis" class="method">
<h4><span title="System.double">double</span> <strong>PopulationKurtosis</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population)</h4>
<div class="content">Evaluates the kurtosis from the full population.
Does not use a normalizer and would thus be biased if applied to a subset (type 1).
Returns NaN if data has less than three entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population</h6>
<p class="comments">The full population data. </p>
</div>
</div>
</div>
<div id="PopulationSkewness" class="method">
<h4><span title="System.double">double</span> <strong>PopulationSkewness</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population)</h4>
<div class="content">Evaluates the skewness from the full population.
Does not use a normalizer and would thus be biased if applied to a subset (type 1).
Returns NaN if data has less than two entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population</h6>
<p class="comments">The full population data. </p>
</div>
</div>
</div>
<div id="PopulationSkewnessKurtosis" class="method">
<h4><span title="System.ValueTuple<double, double>">ValueTuple&lt;double, double&gt;</span> <strong>PopulationSkewnessKurtosis</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population)</h4>
<div class="content">Evaluates the skewness and kurtosis from the full population.
Does not use a normalizer and would thus be biased if applied to a subset (type 1).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population</h6>
<p class="comments">The full population data. </p>
</div>
</div>
</div>
<div id="PopulationStandardDeviation" class="method">
<h4><span title="System.double">double</span> <strong>PopulationStandardDeviation</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population)</h4>
<div class="content">Evaluates the standard deviation from the provided full population.
On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population</h6>
<p class="comments">The full population data. </p>
</div>
</div>
</div>
<div id="PopulationVariance" class="method">
<h4><span title="System.double">double</span> <strong>PopulationVariance</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> population)</h4>
<div class="content">Evaluates the variance from the provided full population.
On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> population</h6>
<p class="comments">The full population data. </p>
</div>
</div>
</div>
<div id="Quantile" class="method">
<h4><span title="System.double">double</span> <strong>Quantile</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.double">double</span> tau)</h4>
<div class="content">Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.double">double</span></code> tau</h6>
<p class="comments">Quantile selector, between 0.0 and 1.0 (inclusive). </p>
</div>
</div>
</div>
<div id="QuantileCustom" class="method">
<h4><span title="System.double">double</span> <strong>QuantileCustom</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.double">double</span> tau, <a href="../MathNet.Numerics.Statistics/QuantileDefinition.htm">QuantileDefinition</a> definition)</h4>
<div class="content">Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.double">double</span></code> tau</h6>
<p class="comments">Quantile selector, between 0.0 and 1.0 (inclusive). </p>
<h6><code><a href="../MathNet.Numerics.Statistics/QuantileDefinition.htm">QuantileDefinition</a></code> definition</h6>
<p class="comments">Quantile definition, to choose what product/definition it should be consistent with </p>
</div>
</div>
</div>
<div id="QuantileCustomFunc" class="method">
<h4><span title="System.Func<double, double>">Func&lt;double, double&gt;</span> <strong>QuantileCustomFunc</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <a href="../MathNet.Numerics.Statistics/QuantileDefinition.htm">QuantileDefinition</a> definition)</h4>
<div class="content">Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><a href="../MathNet.Numerics.Statistics/QuantileDefinition.htm">QuantileDefinition</a></code> definition</h6>
<p class="comments">Quantile definition, to choose what product/definition it should be consistent with </p>
</div>
</div>
</div>
<div id="QuantileFunc" class="method">
<h4><span title="System.Func<double, double>">Func&lt;double, double&gt;</span> <strong>QuantileFunc</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="QuantileRank" class="method">
<h4><span title="System.double">double</span> <strong>QuantileRank</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <span title="System.double">double</span> x, <a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a> definition)</h4>
<div class="content">Estimates the quantile tau from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.double">double</span></code> x</h6>
<p class="comments">Quantile value. </p>
<h6><code><a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a></code> definition</h6>
<p class="comments">Rank definition, to choose how ties should be handled and what product/definition it should be consistent with </p>
</div>
</div>
</div>
<div id="QuantileRank" class="method">
<h4><span title="System.double">double</span> <strong>QuantileRank</strong>(this <span title="System.Collections.Generic.IEnumerable<float>">IEnumerable&lt;float&gt;</span> data, <span title="System.float">float</span> x, <a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a> definition)</h4>
<div class="content">Estimates the quantile tau from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<float>">IEnumerable&lt;float&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><span title="System.float">float</span></code> x</h6>
<p class="comments">Quantile value. </p>
<h6><code><a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a></code> definition</h6>
<p class="comments">Rank definition, to choose how ties should be handled and what product/definition it should be consistent with </p>
</div>
</div>
</div>
<div id="QuantileRankFunc" class="method">
<h4><span title="System.Func<double, double>">Func&lt;double, double&gt;</span> <strong>QuantileRankFunc</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a> definition)</h4>
<div class="content">Estimates the quantile tau from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a></code> definition</h6>
<p class="comments">Rank definition, to choose how ties should be handled and what product/definition it should be consistent with </p>
</div>
</div>
</div>
<div id="Ranks" class="method">
<h4><span title="System.Double[]">Double[]</span> <strong>Ranks</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data, <a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a> definition)</h4>
<div class="content">Evaluates the rank of each entry of the provided samples.
The rank definition can be specified to be compatible
with an existing system.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
<h6><code><a href="../MathNet.Numerics.Statistics/RankDefinition.htm">RankDefinition</a></code> definition</h6>
<p class="comments">Rank definition, to choose how ties should be handled and what product/definition it should be consistent with </p>
</div>
</div>
</div>
<div id="RootMeanSquare" class="method">
<h4><span title="System.double">double</span> <strong>RootMeanSquare</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Evaluates the root mean square (RMS) also known as quadratic mean.
Returns NaN if data is empty or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data to calculate the RMS of. </p>
</div>
</div>
</div>
<div id="Skewness" class="method">
<h4><span title="System.double">double</span> <strong>Skewness</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the unbiased population skewness from the provided samples.
Uses a normalizer (Bessel's correction; type 2).
Returns NaN if data has less than three entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
</div>
</div>
</div>
<div id="SkewnessKurtosis" class="method">
<h4><span title="System.ValueTuple<double, double>">ValueTuple&lt;double, double&gt;</span> <strong>SkewnessKurtosis</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the unbiased population skewness and kurtosis from the provided samples in a single pass.
Uses a normalizer (Bessel's correction; type 2).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
</div>
</div>
</div>
<div id="StandardDeviation" class="method">
<h4><span title="System.double">double</span> <strong>StandardDeviation</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the unbiased population standard deviation from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN if data has less than two entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
</div>
</div>
</div>
<div id="UpperQuartile" class="method">
<h4><span title="System.double">double</span> <strong>UpperQuartile</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> data)</h4>
<div class="content">Estimates the third quartile value from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> data</h6>
<p class="comments">The data sample sequence. </p>
</div>
</div>
</div>
<div id="Variance" class="method">
<h4><span title="System.double">double</span> <strong>Variance</strong>(this <span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span> samples)</h4>
<div class="content">Estimates the unbiased population variance from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN if data has less than two entries or if any entry is NaN.
<div class="parameters">
<h5>Parameters</h5>
<h6><code><span title="System.Collections.Generic.IEnumerable<double>">IEnumerable&lt;double&gt;</span></code> samples</h6>
<p class="comments">A subset of samples, sampled from the full population. </p>
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<p>Based on v5.0.0.0 of MathNet.Numerics (Math.NET Numerics)</p>
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