C# Class MathNet.Numerics.Statistics.VectorArrayStatistics

Pointwise vector statistics on arrays of vectors of the same dimension.

ファイルを表示 Open project: cdrnet/mathnet-numerics

Public Methods

Method	Description
EmpiricalCDF ( this data, double x ) : Vector	Estimates the pointwise empirical cumulative distribution function (CDF) at x from the provided samples.
EmpiricalInvCDF ( this data, double tau ) : Vector	Estimates the pointwise empirical inverse CDF at tau from the provided samples.
Entropy ( this data ) : Vector	Calculates the pointwise entropy of the vectors in bits. Returns NaN if any of the values in the stream are NaN.
InterquartileRange ( this data ) : Vector	Estimates the pointwise inter-quartile range from the vectors. Approximately median-unbiased regardless of the sample distribution (R8).
Kurtosis ( this samples ) : Vector	Estimates the pointwise 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.
LowerQuartile ( this data ) : Vector	Estimates the pointwise first quartile value from the vectors. Approximately median-unbiased regardless of the sample distribution (R8).
Maximum ( this data ) : Vector	Returns the pointwise smallest value from the vectors. Returns NaN if data is empty or any entry is NaN.
Maximum ( this data ) : Vector	Returns the pointwise smallest value from the vectors. Returns NaN if data is empty or any entry is NaN.
Mean ( this data ) : Vector	Estimates the pointwise arithmetic sample mean from the vectors. Returns NaN if data is empty or any entry is NaN.
Median ( this data ) : Vector	Estimates the pointwise median value from the vectors.
Minimum ( this data ) : Vector	Returns the pointwise smallest value of the vectors Returns NaN if data is empty or any entry is NaN.
Minimum ( this data ) : Vector	Returns the pointwise smallest value from the vectors. Returns NaN if data is empty or any entry is NaN.
OrderStatistic ( this data, int order ) : Vector	Returns the pointwise order statistic (order 1..N) from the vectors.
Percentile ( this data, int p ) : Vector	Estimates the pointwise p-Percentile value from the vectors. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8).
PopulationKurtosis ( this population ) : Vector	Evaluates the pointwise 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.
PopulationSkewness ( this population ) : Vector	Evaluates the pointwise 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.
PopulationStandardDeviation ( this population ) : Vector	Evaluates the pointwise population standard deviation from the full population provided as vectors. 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.
PopulationVariance ( this population ) : Vector	Evaluates the pointwise population variance from the full population provided as vectors. 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.
Quantile ( this data, double tau ) : Vector	Estimates the pointwise tau-th quantile from the vectors. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). 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.
QuantileCustom ( this data, double tau, QuantileDefinition definition ) : Vector	Estimates the pointwise tau-th quantile from the vectors. 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.
QuantileCustom ( this data, double tau, double a, double b, double c, double d ) : Vector	Estimates the pointwise tau-th quantile from the vectors. 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.
QuantileRank ( this data, double x, RankDefinition definition = RankDefinition.Default ) : Vector	Estimates the pointwise quantile tau from the vectors. 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.
RootMeanSquare ( this data ) : Vector	Estimates the pointwise root mean square (RMS) also known as quadratic mean from the vectors. Returns NaN if data is empty or any entry is NaN.
Skewness ( this samples ) : Vector	Estimates the pointwise 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.
StandardDeviation ( this samples ) : Vector	Estimates the pointwise unbiased population standard deviation from the provided samples as vectors. 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.
UpperQuartile ( this data ) : Vector	Estimates the pointwise third quartile value from the vectors. Approximately median-unbiased regardless of the sample distribution (R8).
Variance ( this samples ) : Vector	Estimates the pointwise unbiased population variance from the provided samples as vectors. 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.

Method Details

EmpiricalCDF() public static method

Estimates the pointwise empirical cumulative distribution function (CDF) at x from the provided samples.

public static EmpiricalCDF ( this data, double x ) : Vector
data	this	Vector array, where all vectors have the same length.
x	double	The value where to estimate the CDF at.
return	Vector

EmpiricalInvCDF() public static method

Estimates the pointwise empirical inverse CDF at tau from the provided samples.

public static EmpiricalInvCDF ( this data, double tau ) : Vector
data	this	Vector array, where all vectors have the same length.
tau	double	Quantile selector, between 0.0 and 1.0 (inclusive).
return	Vector

Entropy() public static method

Calculates the pointwise entropy of the vectors in bits. Returns NaN if any of the values in the stream are NaN.

public static Entropy ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

InterquartileRange() public static method

Estimates the pointwise inter-quartile range from the vectors. Approximately median-unbiased regardless of the sample distribution (R8).

public static InterquartileRange ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Kurtosis() public static method

Estimates the pointwise 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.

public static Kurtosis ( this samples ) : Vector
samples	this	Vector array, where all vectors have the same length.
return	Vector

LowerQuartile() public static method

Estimates the pointwise first quartile value from the vectors. Approximately median-unbiased regardless of the sample distribution (R8).

public static LowerQuartile ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Maximum() public static method

Returns the pointwise smallest value from the vectors. Returns NaN if data is empty or any entry is NaN.

public static Maximum ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Maximum() public static method

Returns the pointwise smallest value from the vectors. Returns NaN if data is empty or any entry is NaN.

public static Maximum ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Mean() public static method

Estimates the pointwise arithmetic sample mean from the vectors. Returns NaN if data is empty or any entry is NaN.

public static Mean ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Median() public static method

Estimates the pointwise median value from the vectors.

public static Median ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Minimum() public static method

Returns the pointwise smallest value of the vectors Returns NaN if data is empty or any entry is NaN.

public static Minimum ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Minimum() public static method

Returns the pointwise smallest value from the vectors. Returns NaN if data is empty or any entry is NaN.

public static Minimum ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

OrderStatistic() public static method

Returns the pointwise order statistic (order 1..N) from the vectors.

public static OrderStatistic ( this data, int order ) : Vector
data	this	Vector array, where all vectors have the same length.
order	int	One-based order of the statistic, must be between 1 and N (inclusive).
return	Vector

Percentile() public static method

Estimates the pointwise p-Percentile value from the vectors. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8).

public static Percentile ( this data, int p ) : Vector
data	this	Vector array, where all vectors have the same length.
p	int	Percentile selector, between 0 and 100 (inclusive).
return	Vector

PopulationKurtosis() public static method

Evaluates the pointwise 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.

public static PopulationKurtosis ( this population ) : Vector
population	this	Vector array, where all vectors have the same length.
return	Vector

PopulationSkewness() public static method

Evaluates the pointwise 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.

public static PopulationSkewness ( this population ) : Vector
population	this	Vector array, where all vectors have the same length.
return	Vector

PopulationStandardDeviation() public static method

Evaluates the pointwise population standard deviation from the full population provided as vectors. 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.

public static PopulationStandardDeviation ( this population ) : Vector
population	this	Vector array, where all vectors have the same length.
return	Vector

PopulationVariance() public static method

Evaluates the pointwise population variance from the full population provided as vectors. 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.

public static PopulationVariance ( this population ) : Vector
population	this	Vector array, where all vectors have the same length.
return	Vector

Quantile() public static method

Estimates the pointwise tau-th quantile from the vectors. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8).

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.

public static Quantile ( this data, double tau ) : Vector
data	this	Vector array, where all vectors have the same length.
tau	double	Quantile selector, between 0.0 and 1.0 (inclusive).
return	Vector

QuantileCustom() public static method

Estimates the pointwise tau-th quantile from the vectors. 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.

public static QuantileCustom ( this data, double tau, QuantileDefinition definition ) : Vector
data	this	Vector array, where all vectors have the same length.
tau	double	Quantile selector, between 0.0 and 1.0 (inclusive)
definition	QuantileDefinition	Quantile definition, to choose what product/definition it should be consistent with
return	Vector

QuantileCustom() public static method

public static QuantileCustom ( this data, double tau, double a, double b, double c, double d ) : Vector
data	this	Vector array, where all vectors have the same length.
tau	double	Quantile selector, between 0.0 and 1.0 (inclusive)
a	double	a-parameter
b	double	b-parameter
c	double	c-parameter
d	double	d-parameter
return	Vector

QuantileRank() public static method

Estimates the pointwise quantile tau from the vectors. 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.

public static QuantileRank ( this data, double x, RankDefinition definition = RankDefinition.Default ) : Vector
data	this	Vector array, where all vectors have the same length.
x	double	Quantile value.
definition	RankDefinition	Rank definition, to choose how ties should be handled and what product/definition it should be consistent with
return	Vector

RootMeanSquare() public static method

Estimates the pointwise root mean square (RMS) also known as quadratic mean from the vectors. Returns NaN if data is empty or any entry is NaN.

public static RootMeanSquare ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Skewness() public static method

Estimates the pointwise 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.

public static Skewness ( this samples ) : Vector
samples	this	Vector array, where all vectors have the same length.
return	Vector

StandardDeviation() public static method

Estimates the pointwise unbiased population standard deviation from the provided samples as vectors. 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.

public static StandardDeviation ( this samples ) : Vector
samples	this	Vector array, where all vectors have the same length.
return	Vector

UpperQuartile() public static method

Estimates the pointwise third quartile value from the vectors. Approximately median-unbiased regardless of the sample distribution (R8).

public static UpperQuartile ( this data ) : Vector
data	this	Vector array, where all vectors have the same length.
return	Vector

Variance() public static method

Estimates the pointwise unbiased population variance from the provided samples as vectors. 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.

public static Variance ( this samples ) : Vector
samples	this	Vector array, where all vectors have the same length.
return	Vector