##### Parameters

`Single[]`

samples1

First sample array.

`Single[]`

samples2

Second sample array.

- MathNet.Numerics
- MathNet.Numerics.Differentiation
- MathNet.Numerics.Distributions
- MathNet.Numerics.Financial
- MathNet.Numerics.IntegralTransforms
- MathNet.Numerics.Integration
- MathNet.Numerics.Interpolation
- MathNet.Numerics.LinearAlgebra
- MathNet.Numerics.LinearAlgebra.Complex
- MathNet.Numerics.LinearAlgebra.Complex.Solvers
- MathNet.Numerics.LinearAlgebra.Complex32
- MathNet.Numerics.LinearAlgebra.Complex32.Solvers
- MathNet.Numerics.LinearAlgebra.Double
- MathNet.Numerics.LinearAlgebra.Double.Solvers
- MathNet.Numerics.LinearAlgebra.Factorization
- MathNet.Numerics.LinearAlgebra.Single
- MathNet.Numerics.LinearAlgebra.Single.Solvers
- MathNet.Numerics.LinearAlgebra.Solvers
- MathNet.Numerics.LinearAlgebra.Storage
- MathNet.Numerics.LinearRegression
- MathNet.Numerics.OdeSolvers
- MathNet.Numerics.Optimization
- MathNet.Numerics.Optimization.LineSearch
- MathNet.Numerics.Optimization.ObjectiveFunctions
- MathNet.Numerics.Properties
- MathNet.Numerics.Providers.Common.Cuda
- MathNet.Numerics.Providers.Common.Mkl
- MathNet.Numerics.Providers.Common.OpenBlas
- MathNet.Numerics.Providers.FourierTransform
- MathNet.Numerics.Providers.LinearAlgebra
- MathNet.Numerics.Providers.LinearAlgebra.OpenBlas
- MathNet.Numerics.Random
- MathNet.Numerics.RootFinding
- MathNet.Numerics.Statistics
- MathNet.Numerics.Statistics.Mcmc

**Type** ArrayStatistics

**Namespace** MathNet.Numerics.Statistics

Statistics operating on arrays assumed to be unsorted.
WARNING: Methods with the Inplace-suffix may modify the data array by reordering its entries.

- Covariance
- Covariance
- Covariance
- FiveNumberSummaryInplace
- FiveNumberSummaryInplace
- GeometricMean
- GeometricMean
- GeometricMean
- HarmonicMean
- HarmonicMean
- HarmonicMean
- InterquartileRangeInplace
- InterquartileRangeInplace
- LowerQuartileInplace
- LowerQuartileInplace
- Maximum
- Maximum
- MaximumAbsolute
- MaximumAbsolute
- MaximumMagnitudePhase
- MaximumMagnitudePhase
- Mean
- Mean
- Mean
- MeanStandardDeviation
- MeanStandardDeviation
- MeanStandardDeviation
- MeanVariance
- MeanVariance
- MeanVariance
- MedianInplace
- MedianInplace
- Minimum
- Minimum
- MinimumAbsolute
- MinimumAbsolute
- MinimumMagnitudePhase
- MinimumMagnitudePhase
- OrderStatisticInplace
- OrderStatisticInplace
- PercentileInplace
- PercentileInplace
- PopulationCovariance
- PopulationCovariance
- PopulationCovariance
- PopulationStandardDeviation
- PopulationStandardDeviation
- PopulationStandardDeviation
- PopulationVariance
- PopulationVariance
- PopulationVariance
- QuantileCustomInplace
- QuantileCustomInplace
- QuantileCustomInplace
- QuantileCustomInplace
- QuantileInplace
- QuantileInplace
- RanksInplace
- RanksInplace
- RootMeanSquare
- RootMeanSquare
- RootMeanSquare
- StandardDeviation
- StandardDeviation
- StandardDeviation
- UpperQuartileInplace
- UpperQuartileInplace
- Variance
- Variance
- Variance

Estimates the unbiased population covariance from the provided two sample arrays.
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.
##### Parameters

`Single[]`

samples1First sample array.

`Single[]`

samples2Second sample array.

Estimates the unbiased population covariance from the provided two sample arrays.
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.
##### Parameters

`Double[]`

samples1First sample array.

`Double[]`

samples2Second sample array.

Estimates the unbiased population covariance from the provided two sample arrays.
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.
##### Parameters

`Int32[]`

samples1First sample array.

`Int32[]`

samples2Second sample array.

Estimates {min, lower-quantile, median, upper-quantile, max} from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates {min, lower-quantile, median, upper-quantile, max} from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

Evaluates the geometric mean of the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Evaluates the geometric mean of the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Int32[]`

dataSample array, no sorting is assumed.

Evaluates the geometric mean of the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Evaluates the harmonic mean of the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Int32[]`

dataSample array, no sorting is assumed.

Evaluates the harmonic mean of the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Evaluates the harmonic mean of the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Estimates the inter-quartile range from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates the inter-quartile range from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates the first quartile value from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates the first quartile value from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

Returns the largest value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Returns the smallest value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Returns the largest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Returns the largest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Returns the largest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Complex32[]`

dataSample array, no sorting is assumed.

Returns the largest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Complex[]`

dataSample array, no sorting is assumed.

Estimates the arithmetic sample mean from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Estimates the arithmetic sample mean from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Int32[]`

dataSample array, no sorting is assumed.

Estimates the arithmetic sample mean from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Estimates the arithmetic sample mean and the unbiased population standard deviation from the provided samples as unsorted array.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN.
##### Parameters

`Single[]`

samplesSample array, no sorting is assumed.

Estimates the arithmetic sample mean and the unbiased population standard deviation from the provided samples as unsorted array.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN.
##### Parameters

`Int32[]`

samplesSample array, no sorting is assumed.

Estimates the arithmetic sample mean and the unbiased population standard deviation from the provided samples as unsorted array.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN.
##### Parameters

`Double[]`

samplesSample array, no sorting is assumed.

Estimates the arithmetic sample mean and the unbiased population variance from the provided samples as unsorted array.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN.
##### Parameters

`Single[]`

samplesSample array, no sorting is assumed.

Estimates the arithmetic sample mean and the unbiased population variance from the provided samples as unsorted array.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN.
##### Parameters

`Double[]`

samplesSample array, no sorting is assumed.

Estimates the arithmetic sample mean and the unbiased population variance from the provided samples as unsorted array.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN.
##### Parameters

`Int32[]`

samplesSample array, no sorting is assumed.

Estimates the median value from the unsorted data array.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates the median value from the unsorted data array.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

Returns the smallest value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Returns the smallest value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Returns the smallest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Returns the smallest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Returns the smallest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Complex[]`

dataSample array, no sorting is assumed.

Returns the smallest absolute value from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Complex32[]`

dataSample array, no sorting is assumed.

Returns the order statistic (order 1..N) from the unsorted data array.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

`int`

orderOne-based order of the statistic, must be between 1 and N (inclusive).

Returns the order statistic (order 1..N) from the unsorted data array.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

`int`

orderOne-based order of the statistic, must be between 1 and N (inclusive).

Estimates the p-Percentile value from the unsorted data array.
If a non-integer Percentile is needed, use Quantile instead.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

`int`

pPercentile selector, between 0 and 100 (inclusive).

Estimates the p-Percentile value from the unsorted data array.
If a non-integer Percentile is needed, use Quantile instead.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

`int`

pPercentile selector, between 0 and 100 (inclusive).

Evaluates the population covariance from the full population provided as two arrays.
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.
##### Parameters

`Double[]`

population1First population array.

`Double[]`

population2Second population array.

Evaluates the population covariance from the full population provided as two arrays.
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.
##### Parameters

`Int32[]`

population1First population array.

`Int32[]`

population2Second population array.

Evaluates the population covariance from the full population provided as two arrays.
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.
##### Parameters

`Single[]`

population1First population array.

`Single[]`

population2Second population array.

Evaluates the population standard deviation from the full population provided as unsorted array.
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.
##### Parameters

`Double[]`

populationSample array, no sorting is assumed.

Evaluates the population standard deviation from the full population provided as unsorted array.
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.
##### Parameters

`Int32[]`

populationSample array, no sorting is assumed.

Evaluates the population standard deviation from the full population provided as unsorted array.
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.
##### Parameters

`Single[]`

populationSample array, no sorting is assumed.

Evaluates the population variance from the full population provided as unsorted array.
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.
##### Parameters

`Double[]`

populationSample array, no sorting is assumed.

Evaluates the population variance from the full population provided as unsorted array.
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.
##### Parameters

`Int32[]`

populationSample array, no sorting is assumed.

Evaluates the population variance from the full population provided as unsorted array.
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.
##### Parameters

`Single[]`

populationSample array, no sorting is assumed.

Estimates the tau-th quantile from the unsorted data array.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified
by 4 parameters a, b, c and d, consistent with Mathematica.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

`double`

tauQuantile selector, between 0.0 and 1.0 (inclusive)

`double`

aa-parameter

`double`

bb-parameter

`double`

cc-parameter

`double`

dd-parameter

Estimates the tau-th quantile from the unsorted data array.
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.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

`double`

tauQuantile selector, between 0.0 and 1.0 (inclusive)

`QuantileDefinition`

definitionQuantile definition, to choose what product/definition it should be consistent with

Estimates the tau-th quantile from the unsorted data array.
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.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

`double`

tauQuantile selector, between 0.0 and 1.0 (inclusive)

`QuantileDefinition`

definitionQuantile definition, to choose what product/definition it should be consistent with

Estimates the tau-th quantile from the unsorted data array.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified
by 4 parameters a, b, c and d, consistent with Mathematica.
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

`double`

tauQuantile selector, between 0.0 and 1.0 (inclusive)

`double`

aa-parameter

`double`

bb-parameter

`double`

cc-parameter

`double`

dd-parameter

Estimates the tau-th quantile from the unsorted data array.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

R-8, SciPy-(1/3,1/3): Linear interpolation of the approximate medians for order statistics. When tau < (2/3) / (N + 1/3), use x1. When tau >= (N - 1/3) / (N + 1/3), use xN.

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

`double`

tauQuantile selector, between 0.0 and 1.0 (inclusive).

Estimates the tau-th quantile from the unsorted data array.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

R-8, SciPy-(1/3,1/3): Linear interpolation of the approximate medians for order statistics. When tau < (2/3) / (N + 1/3), use x1. When tau >= (N - 1/3) / (N + 1/3), use xN.

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

`double`

tauQuantile selector, between 0.0 and 1.0 (inclusive).

Evaluates the rank of each entry of the unsorted data array.
The rank definition can be specified to be compatible
with an existing system.
WARNING: Works inplace and can thus causes the data array to be reordered.

Evaluates the rank of each entry of the unsorted data array.
The rank definition can be specified to be compatible
with an existing system.
WARNING: Works inplace and can thus causes the data array to be reordered.

Estimates the root mean square (RMS) also known as quadratic mean from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Int32[]`

dataSample array, no sorting is assumed.

Estimates the root mean square (RMS) also known as quadratic mean from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed.

Estimates the root mean square (RMS) also known as quadratic mean from the unsorted data array.
Returns NaN if data is empty or any entry is NaN.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed.

Estimates the unbiased population standard deviation from the provided samples as unsorted array.
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.
##### Parameters

`Int32[]`

samplesSample array, no sorting is assumed.

Estimates the unbiased population standard deviation from the provided samples as unsorted array.
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.
##### Parameters

`Single[]`

samplesSample array, no sorting is assumed.

Estimates the unbiased population standard deviation from the provided samples as unsorted array.
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.
##### Parameters

`Double[]`

samplesSample array, no sorting is assumed.

Estimates the third quartile value from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Double[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates the third quartile value from the unsorted data array.
Approximately median-unbiased regardless of the sample distribution (R8).
WARNING: Works inplace and can thus causes the data array to be reordered.
##### Parameters

`Single[]`

dataSample array, no sorting is assumed. Will be reordered.

Estimates the unbiased population variance from the provided samples as unsorted array.
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.
##### Parameters

`Int32[]`

samplesSample array, no sorting is assumed.

Estimates the unbiased population variance from the provided samples as unsorted array.
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.
##### Parameters

`Single[]`

samplesSample array, no sorting is assumed.

Estimates the unbiased population variance from the provided samples as unsorted array.
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.
##### Parameters

`Double[]`

samplesSample array, no sorting is assumed.