Collaboration diagram for Basic statistics:

Classes
struct	JKQTPStat5NumberStatistics
	represents the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) More...

Functions
template<class InputIt>
void	jkqtpstat5NumberStatistics (InputIt first, InputIt last, double minimum, double minimumQuantile=0, double median=nullptr, double maximum=nullptr, double maximumQuantile=1, double quantile1Spec=0.25, double quantile1=nullptr, double quantile2Spec=0.75, double quantile2=nullptr, double IQR=nullptr, double IQRSignificance=nullptr, size_t Noutput=nullptr)
	calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a given data range first ... last (5-value statistics, e.g. used for boxplots)
template<class InputIt>
JKQTPStat5NumberStatistics	jkqtpstat5NumberStatistics (InputIt first, InputIt last, double quantile1Spec=0.25, double quantile2Spec=0.75, double minimumQuantile=0, double maximumQuantile=1.0)
	calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a given data range first ... last (5-value statistics, e.g. used for boxplots)
template<class InputIt, class OutputIt>
void	jkqtpstat5NumberStatisticsAndOutliers (InputIt first, InputIt last, OutputIt outliersout, double minimum=nullptr, double minimumQuantile=0, double median=nullptr, double maximum=nullptr, double maximumQuantile=1, double quantile1=nullptr, double quantile1Spec=0.25, double quantile2=nullptr, double quantile2Spec=0.75, double IQR=nullptr, double IQRSignificance=nullptr, size_t Noutput=nullptr)
	calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a given data range first ... last (5-value statistics, e.g. used for boxplots)
template<class TVector, class OutputIt>
void	jkqtpstat5NumberStatisticsAndOutliersOfSortedVector (const TVector &data, OutputIt outliersout, double minimum=nullptr, double minimumQuantile=0, double median=nullptr, double maximum=nullptr, double maximumQuantile=1, double quantile1=nullptr, double quantile1Spec=0.25, double quantile2=nullptr, double quantile2Spec=0.75, double IQR=nullptr, double IQRSignificance=nullptr, size_t Noutput=nullptr)
	calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a sorted vector
template<class TVector>
void	jkqtpstat5NumberStatisticsOfSortedVector (const TVector &data, double minimum=nullptr, double minimumQuantile=0, double median=nullptr, double maximum=nullptr, double maximumQuantile=1, double quantile1=nullptr, double quantile1Spec=0.25, double quantile2=nullptr, double quantile2Spec=0.75, double IQR=nullptr, double IQRSignificance=nullptr, size_t Noutput=nullptr)
	calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a sorted vector
template<class InputIt>
double	jkqtpstatAverage (InputIt first, InputIt last, size_t *Noutput=nullptr)
	calculates the average of a given data range first ... last
template<class InputIt>
double	jkqtpstatCentralMoment (InputIt first, InputIt last, int order, double averageOut=nullptr, size_t Noutput=nullptr)
	calculates the given central moment $\langle (X-\mu)^o\rangle$ of a given data range first ... last
template<class InputIt1, class InputIt2>
double	jkqtpstatCorrelationCoefficient (InputIt1 first1, InputIt1 last1, InputIt2 first2, double averageOut1=nullptr, double averageOut2=nullptr, size_t *Noutput=nullptr)
	calculate empirical (Pearson's) correlation coefficient $\rho_{x,y}$ between two given data ranges first1 ... last1 and first2 ... last2
template<class InputIt>
size_t	jkqtpstatCount (InputIt first, InputIt last)
	calculates the number of valid values in the given data range first ... last
template<class InputIt, class OutputIt>
void	jkqtpstatCumSum (InputIt first, InputIt last, OutputIt output)
	calculates the vector of cummulative (or partial) sums of a given data range first ... last
template<class InputIt, class OutputIt>
size_t	jkqtpstatFilterGoodFloat (InputIt first, InputIt last, OutputIt output)
	filters the given data range first ... last for good floats (using JKQTPIsOKFloat() )
template<class InputIt>
double	jkqtpstatMAD (InputIt first, InputIt last, double median=nullptr, size_t Noutput=nullptr)
	calculates the median absolute deviation about the median (MAD) of a given data range first ... last
template<class InputIt>
double	jkqtpstatMaximum (InputIt first, InputIt last, InputIt maxPos=nullptr, size_t Noutput=nullptr)
	calculates the maximum value in the given data range first ... last
template<class InputIt>
double	jkqtpstatMedian (InputIt first, InputIt last, size_t *Noutput=nullptr)
	calculates the median of a given data range first ... last
template<class InputIt>
double	jkqtpstatMedianAndPartialSort (InputIt first, InputIt last)
	calculates the median of a given data range first ... last, this version partially sorts the range (i.e. no internal copy and checking for NAN-values is performed!)
template<class TVector>
double	jkqtpstatMedianOfSortedVector (const TVector &data, size_t *Noutput=nullptr)
	calculates the median of a given sorted (!) data vector
template<class InputIt>
double	jkqtpstatMinimum (InputIt first, InputIt last, InputIt minPos=nullptr, size_t Noutput=nullptr)
	calculates the minimum value in the given data range first ... last
template<class InputIt>
void	jkqtpstatMinMax (InputIt first, InputIt last, double &min, double &max, InputIt minPos=nullptr, InputIt maxPos=nullptr, size_t *Noutput=nullptr)
	calculates the minimum and maximum values in the given data range first ... last
template<class InputIt, class FF>
double	jkqtpstatModifiedSum (InputIt first, InputIt last, FF modifierFunctor, size_t *Noutput=nullptr)
	calculates the sum of a given data range first ... last of values, modifying each value with a given functor modifierFunctor before accumulating
template<class InputIt>
double	jkqtpstatMoment (InputIt first, InputIt last, int order, size_t *Noutput=nullptr)
	calculates the given (non-central) moment $\langle X^o\rangle$ of a given data range first ... last
template<class InputIt>
double	jkqtpstatNMAD (InputIt first, InputIt last, double median=nullptr, size_t Noutput=nullptr)
	calculates the normalized median absolute deviation about the median (NMAD) of a given data range first ... last
template<class InputIt>
double	jkqtpstatQuantile (InputIt first, InputIt last, double quantile, size_t *Noutput=nullptr)
	calculates the quantile -th quantile of a given data range first ... last
template<class InputIt>
double	jkqtpstatSkewness (InputIt first, InputIt last, double averageOut=nullptr, size_t Noutput=nullptr)
	calculates the skewness $\gamma_1=\mathbb{E}\left[\left(\frac{X-\mu}{\sigma}\right)^3\right]$ of a given data range first ... last
template<class InputIt>
double	jkqtpstatStdDev (InputIt first, InputIt last, double averageOut=nullptr, size_t Noutput=nullptr)
	calculates the standard deviation $\sigma_X=\sqrt{\mbox{Var}(X)}$ of a given data range first ... last
template<class InputIt>
double	jkqtpstatSum (InputIt first, InputIt last, size_t *Noutput=nullptr)
	calculates the sum of a given data range first ... last
template<class InputIt>
double	jkqtpstatSumSqr (InputIt first, InputIt last, size_t *Noutput=nullptr)
	calculates the sum of squares of a given data range first ... last
template<class InputIt>
double	jkqtpstatVariance (InputIt first, InputIt last, double averageOut=nullptr, size_t Noutput=nullptr)
	calculates the variance $\sigma_X^2=\mbox{Var}(X)$ of a given data range first ... last
template<class InputIt, class InputWeightIt>
double	jkqtpstatWeightedAverage (InputIt first, InputIt last, InputWeightIt firstWeight, size_t *Noutput=nullptr)
	calculates the weighted average of a given data range first ... last
template<class InputIt, class InputWeightIt>
double	jkqtpstatWeightedStdDev (InputIt first, InputIt last, InputWeightIt firstWeight, double averageOut=nullptr, size_t Noutput=nullptr)
	calculates the weighted standard deviation $\sigma_X=\sqrt{\mbox{Var}(X)}$ of a given data range first ... last
template<class InputIt, class InputWeightIt>
double	jkqtpstatWeightedVariance (InputIt first, InputIt last, InputWeightIt firstWeight, double averageOut=nullptr, size_t Noutput=nullptr)
	calculates the weighted variance $\sigma_X^2=\mbox{Var}(X)$ of a given data range first ... last

Detailed Description

Function Documentation

◆ jkqtpstat5NumberStatistics() [1/2]

template<class InputIt>

void jkqtpstat5NumberStatistics	(	InputIt	first,
		InputIt	last,
		double *	minimum,
		double	minimumQuantile = 0,
		double *	median = nullptr,
		double *	maximum = nullptr,
		double	maximumQuantile = 1,
		double	quantile1Spec = 0.25,
		double *	quantile1 = nullptr,
		double	quantile2Spec = 0.75,
		double *	quantile2 = nullptr,
		double *	IQR = nullptr,
		double *	IQRSignificance = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a given data range first ... last (5-value statistics, e.g. used for boxplots)

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	minimum	optionally returns the minimum value of the array
	minimumQuantile	specifies a quantile for the return value minimum (default is 0 for the real minimum, but you could e.g. use 0.05 for the 5% quantile!
[out]	median	optionally returns the median value of the array
[out]	maximum	optionally returns the maximum value of the array
	maximumQuantile	specifies a quantile for the return value maximum (default is 1 for the real maximum, but you could e.g. use 0.95 for the 95% quantile!
	quantile1Spec	specifies which quantile to calculate for qantile1 (range: 0..1)
[out]	quantile1	optionally returns the first quantile of the array (specified by quantile1Spec )
	quantile2Spec	specifies which quantile to calculate for qantile2 (range: 0..1)
[out]	quantile2	optionally returns the second quantile of the array (specified by quantile2Spec )
[out]	IQR	interquartile range, i.e. the range between quantile1 and quantile2
[out]	IQRSignificance	significance range of the interquartile range, calculated as $2\cdot\frac{1.58\cdot \mbox{IQR}}{\sqrt{N}}$

See also: https://en.wikipedia.org/wiki/Box_plot

Parameters

[out] Noutput optionally returns the number of accumulated valid values in this variable

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Five-number_summary, jkqtpstatAddVBoxplotAndOutliers, jkqtpstatAddHBoxplotAndOutliers, jkqtpstatAddVBoxplot, jkqtpstatAddHBoxplot, Tutorial (JKQTPDatastore): Advanced 1-Dimensional Statistics with JKQTPDatastore

◆ jkqtpstat5NumberStatistics() [2/2]

template<class InputIt>

JKQTPStat5NumberStatistics jkqtpstat5NumberStatistics	(	InputIt	first,
		InputIt	last,
		double	quantile1Spec = 0.25,
		double	quantile2Spec = 0.75,
		double	minimumQuantile = 0,
		double	maximumQuantile = 1.0 )

inline

calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a given data range first ... last (5-value statistics, e.g. used for boxplots)

Template Parameters

InputIt standard iterator type of first and last.

Parameters

first	iterator pointing to the first item in the dataset to use
last	iterator pointing behind the last item in the dataset to use
quantile1Spec	specifies which quantile to calculate for qantile1 (range: 0..1)
quantile2Spec	specifies which quantile to calculate for qantile2 (range: 0..1)
minimumQuantile	specifies a quantile for the return value minimum (default is 0 for the real minimum, but you could e.g. use 0.05 for the 5% quantile!)
maximumQuantile	specifies a quantile for the return value maximum (default is 1 for the real maximum, but you could e.g. use 0.95 for the 95% quantile!)

Returns: the Five-Number Statistical Summary in a JKQTPStat5NumberStatistics

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Five-number_summary, jkqtpstatAddVBoxplotAndOutliers, jkqtpstatAddHBoxplotAndOutliers, jkqtpstatAddVBoxplot, jkqtpstatAddHBoxplot, Tutorial (JKQTPDatastore): Advanced 1-Dimensional Statistics with JKQTPDatastore

◆ jkqtpstat5NumberStatisticsAndOutliers()

template<class InputIt, class OutputIt>

void jkqtpstat5NumberStatisticsAndOutliers	(	InputIt	first,
		InputIt	last,
		OutputIt	outliersout,
		double *	minimum = nullptr,
		double	minimumQuantile = 0,
		double *	median = nullptr,
		double *	maximum = nullptr,
		double	maximumQuantile = 1,
		double *	quantile1 = nullptr,
		double	quantile1Spec = 0.25,
		double *	quantile2 = nullptr,
		double	quantile2Spec = 0.75,
		double *	IQR = nullptr,
		double *	IQRSignificance = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a given data range first ... last (5-value statistics, e.g. used for boxplots)

Template Parameters

InputIt	standard iterator type of first and last.
OutputIt	standard output iterator type used for the outliers output outliersout, use e.g. std::back_inserter

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	outliersout	output iterator that receives the outliers, smaller than minimum and larger than maximum
[out]	minimum	optionally returns the minimum value of the array
	minimumQuantile	specifies a quantile for the return value minimum (default is 0 for the real minimum, but you could e.g. use 0.05 for the 5% quantile!)
[out]	median	optionally returns the median value of the array
[out]	maximum	optionally returns the maximum value of the array
	maximumQuantile	specifies a quantile for the return value maximum (default is 1 for the real maximum, but you could e.g. use 0.95 for the 95% quantile!)
	quantile1Spec	specifies which quantile to calculate for qantile1 (range: 0..1)
[out]	quantile1	optionally returns the first quantile of the array (specified by quantile1Spec )
	quantile2Spec	specifies which quantile to calculate for qantile2 (range: 0..1)
[out]	quantile2	optionally returns the second quantile of the array (specified by quantile2Spec )
[out]	IQR	interquartile range, i.e. the range between quantile1 and quantile2
[out]	IQRSignificance	significance range of the interquartile range, calculated as $2\cdot\frac{1.58\cdot \mbox{IQR}}{\sqrt{N}}$

See also: https://en.wikipedia.org/wiki/Box_plot

Parameters

[out] Noutput optionally returns the number of accumulated valid values in this variable

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Five-number_summary, jkqtpstatAddVBoxplotAndOutliers, jkqtpstatAddHBoxplotAndOutliers, jkqtpstatAddVBoxplot, jkqtpstatAddHBoxplot, Tutorial (JKQTPDatastore): Advanced 1-Dimensional Statistics with JKQTPDatastore

◆ jkqtpstat5NumberStatisticsAndOutliersOfSortedVector()

template<class TVector, class OutputIt>

void jkqtpstat5NumberStatisticsAndOutliersOfSortedVector	(	const TVector &	data,
		OutputIt	outliersout,
		double *	minimum = nullptr,
		double	minimumQuantile = 0,
		double *	median = nullptr,
		double *	maximum = nullptr,
		double	maximumQuantile = 1,
		double *	quantile1 = nullptr,
		double	quantile1Spec = 0.25,
		double *	quantile2 = nullptr,
		double	quantile2Spec = 0.75,
		double *	IQR = nullptr,
		double *	IQRSignificance = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a sorted vector

Template Parameters

TVector a type, compatible with std::vector (i,e, providing size(), []-element access and iterators)

Parameters

	data	a sorted vector with values
	outliersout	output iterator that receives the outliers, smaller than minimum and larger than maximum
[out]	minimum	optionally returns the minimum value of the array
	minimumQuantile	specifies a quantile for the return value minimum (default is 0 for the real minimum, but you could e.g. use 0.05 for the 5% quantile!)
[out]	median	optionally returns the median value of the array
[out]	maximum	optionally returns the maximum value of the array
	maximumQuantile	specifies a quantile for the return value maximum (default is 1 for the real maximum, but you could e.g. use 0.95 for the 95% quantile!)
	quantile1Spec	specifies which quantile to calculate for qantile1 (range: 0..1)
[out]	quantile1	optionally returns the first quantile of the array (specified by quantile1Spec )
	quantile2Spec	specifies which quantile to calculate for qantile2 (range: 0..1)
[out]	quantile2	optionally returns the second quantile of the array (specified by quantile2Spec )
[out]	IQR	interquartile range, i.e. the range between quantile1 and quantile2
[out]	IQRSignificance	significance range of the interquartile range, calculated as $2\cdot\frac{1.58\cdot \mbox{IQR}}{\sqrt{N}}$

See also: https://en.wikipedia.org/wiki/Box_plot

Parameters

[out] Noutput optionally returns the number of accumulated valid values in this variable

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Five-number_summary, jkqtpstatAddVBoxplotAndOutliers, jkqtpstatAddHBoxplotAndOutliers, jkqtpstatAddVBoxplot, jkqtpstatAddHBoxplot, Tutorial (JKQTPDatastore): Advanced 1-Dimensional Statistics with JKQTPDatastore

◆ jkqtpstat5NumberStatisticsOfSortedVector()

template<class TVector>

void jkqtpstat5NumberStatisticsOfSortedVector	(	const TVector &	data,
		double *	minimum = nullptr,
		double	minimumQuantile = 0,
		double *	median = nullptr,
		double *	maximum = nullptr,
		double	maximumQuantile = 1,
		double *	quantile1 = nullptr,
		double	quantile1Spec = 0.25,
		double *	quantile2 = nullptr,
		double	quantile2Spec = 0.75,
		double *	IQR = nullptr,
		double *	IQRSignificance = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the Five-Number Statistical Summary (minimum, median, maximum and two user-defined quantiles (as well as derived from these the inter quartile range)) of a sorted vector

Template Parameters

TVector a type, compatible with std::vector (i,e, providing size(), []-element access and iterators)

Parameters

	data	a sorted vector with values
[out]	minimum	optionally returns the minimum value of the array
	minimumQuantile	specifies a quantile for the return value minimum (default is 0 for the real minimum, but you could e.g. use 0.05 for the 5% quantile!
[out]	median	optionally returns the median value of the array
[out]	maximum	optionally returns the maximum value of the array
	maximumQuantile	specifies a quantile for the return value maximum (default is 1 for the real maximum, but you could e.g. use 0.95 for the 95% quantile!
	quantile1Spec	specifies which quantile to calculate for qantile1 (range: 0..1)
[out]	quantile1	optionally returns the first quantile of the array (specified by quantile1Spec )
	quantile2Spec	specifies which quantile to calculate for qantile2 (range: 0..1)
[out]	quantile2	optionally returns the second quantile of the array (specified by quantile2Spec )
[out]	IQR	interquartile range, i.e. the range between quantile1 and quantile2
[out]	IQRSignificance	significance range of the interquartile range, calculated as $2\cdot\frac{1.58\cdot \mbox{IQR}}{\sqrt{N}}$

See also: https://en.wikipedia.org/wiki/Box_plot

Parameters

[out] Noutput optionally returns the number of accumulated valid values in this variable

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Five-number_summary, jkqtpstatAddVBoxplotAndOutliers, jkqtpstatAddHBoxplotAndOutliers, jkqtpstatAddVBoxplot, jkqtpstatAddHBoxplot, Tutorial (JKQTPDatastore): Advanced 1-Dimensional Statistics with JKQTPDatastore

◆ jkqtpstatAverage()

template<class InputIt>

double jkqtpstatAverage	(	InputIt	first,
		InputIt	last,
		size_t *	Noutput = nullptr )

inline

calculates the average of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: Average of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

This function implements:

$\overline{X}=\frac{1}{N}\cdot\sum\limits_{i=1}^{N}X_i$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatCentralMoment()

template<class InputIt>

double jkqtpstatCentralMoment	(	InputIt	first,
		InputIt	last,
		int	order,
		double *	averageOut = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the given central moment $\langle (X-\mu)^o\rangle$ of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	order	oder of the central moment $\langle (X-\mu)^o\rangle$
[out]	averageOut	returns (optionally) the average of the dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the given central moment $\langle (X-\mu)^o\rangle$ of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\langle (X-\mu)^o\rangle= \mathbb{E}\left[\left(X-\mu\right)^o\right]$

where $\mu$ is the mean of a random variable and $\overline{x}$ is the average (calculated using jkqtpstatAverage() ) of the input dataset .

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatCorrelationCoefficient()

template<class InputIt1, class InputIt2>

double jkqtpstatCorrelationCoefficient	(	InputIt1	first1,
		InputIt1	last1,
		InputIt2	first2,
		double *	averageOut1 = nullptr,
		double *	averageOut2 = nullptr,
		size_t *	Noutput = nullptr )

inline

calculate empirical (Pearson's) correlation coefficient $\rho_{x,y}$ between two given data ranges first1 ... last1 and first2 ... last2

Template Parameters

InputIt1	standard iterator type of first1 and last1.
InputIt2	standard iterator type of first2 and last2.

Parameters

	first1	iterator pointing to the first item in the first dataset to use
	last1	iterator pointing behind the last item in the first dataset to use
	first2	iterator pointing to the second item in the first dataset to use
[out]	averageOut1	returns (optionally) the average of the first dataset
[out]	averageOut2	returns (optionally) the average of the second dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: pearson's correlation coefficient If the given range first1 ... last1 is empty, JKQTP_DOUBLE_NAN is returned

This function implements:

$\rho_{x,y}=\text{CorCoeff}_{\text{Pearson}}(x,y)=\frac{\sum\limits_{i=0}^{N-1}(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum\limits_{i=0}^{N-1}(x_i-\overline{x})^2\cdot\sum\limits_{i=0}^{N-1}(y_i-\overline{y})^2}}$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

◆ jkqtpstatCount()

template<class InputIt>

size_t jkqtpstatCount	(	InputIt	first,
		InputIt	last )

inline

calculates the number of valid values in the given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

first	iterator pointing to the first item in the dataset to use
last	iterator pointing behind the last item in the dataset to use

Returns: number of valid values between first and last (excluding invalid doubles).

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatCumSum()

template<class InputIt, class OutputIt>

void jkqtpstatCumSum	(	InputIt	first,
		InputIt	last,
		OutputIt	output )

inline

calculates the vector of cummulative (or partial) sums of a given data range first ... last

Template Parameters

InputIt	standard iterator type of first and last.
OutputIt	standard output iterator type

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	output	This iterator is used to store the results, use e.g. a std::back_inserter Output is then a vector of cummulative (or partial) sums returned between first and last (excluding invalid doubles). For invalid values, the last sum is re-inserted, so the returned vector has the same number of entries as the range first ... last

This function implements:

$\sum(X)_j=\cdot\sum\limits_{i=1}^{j}X_i$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatFilterGoodFloat()

template<class InputIt, class OutputIt>

size_t jkqtpstatFilterGoodFloat	(	InputIt	first,
		InputIt	last,
		OutputIt	output )

inline

filters the given data range first ... last for good floats (using JKQTPIsOKFloat() )

Template Parameters

InputIt	standard iterator type of first and last.
OutputIt	standard output iterator type

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	output	This iterator is used to store the results, use e.g. a std::back_inserter

Returns: number of elementes put into output

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatMAD()

template<class InputIt>

double jkqtpstatMAD	(	InputIt	first,
		InputIt	last,
		double *	median = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the median absolute deviation about the median (MAD) of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	median	optionally returns the median value in this variable
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the median absolute deviation about the median (MAD) of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

This function calculates

$\mbox{MAD}(\vec{x})=\mbox{Med}\left\{|\vec{x}-\mbox{Med}(\vec{x})|\right\}$

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Median_absolute_deviation and Ricardo A. Maronna, R. Douglas Martin, Victor J. Yohai: "Robust Statistics: Theory and Methods", Wiley, 2006, ISBN: 978-0-470-01092-1

◆ jkqtpstatMaximum()

template<class InputIt>

double jkqtpstatMaximum	(	InputIt	first,
		InputIt	last,
		InputIt *	maxPos = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the maximum value in the given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	maxPos	receives the location of the maximum element value
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the maximum value from the given range

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatMedian()

template<class InputIt>

double jkqtpstatMedian	(	InputIt	first,
		InputIt	last,
		size_t *	Noutput = nullptr )

inline

calculates the median of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the median of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

Note: This operation implies an internal copy of the data, and then uses std::nth_element() to calculate the median in linear time O(N)!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatMedianAndPartialSort()

template<class InputIt>

double jkqtpstatMedianAndPartialSort	(	InputIt	first,
		InputIt	last )

inline

calculates the median of a given data range first ... last, this version partially sorts the range (i.e. no internal copy and checking for NAN-values is performed!)

Template Parameters

InputIt standard iterator type of first and last.

Parameters

first	iterator pointing to the first item in the dataset to use
last	iterator pointing behind the last item in the dataset to use

Returns: the median of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

Note: This operation implies uses std::nth_element() to calculate the median in linear time O(N)! The given range is partially sorted after the call!

◆ jkqtpstatMedianOfSortedVector()

template<class TVector>

double jkqtpstatMedianOfSortedVector	(	const TVector &	data,
		size_t *	Noutput = nullptr )

inline

calculates the median of a given sorted (!) data vector

Template Parameters

TVector a type, compatible with std::vector (i,e, providing size(), []-element access and iterators)

Parameters

	data	a sorted vector with values
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the median of data If data is empty, NAN is returned

◆ jkqtpstatMinimum()

template<class InputIt>

double jkqtpstatMinimum	(	InputIt	first,
		InputIt	last,
		InputIt *	minPos = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the minimum value in the given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	minPos	receives the location of the minimum element value
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the minimum value from the given range

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatMinMax()

template<class InputIt>

void jkqtpstatMinMax	(	InputIt	first,
		InputIt	last,
		double &	min,
		double &	max,
		InputIt *	minPos = nullptr,
		InputIt *	maxPos = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the minimum and maximum values in the given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	min	receives the minimum element value
[out]	max	receives the maximum element value
[out]	minPos	receives the location of the minimum element value
[out]	maxPos	receives the location of the minimum maximum element value
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatModifiedSum()

template<class InputIt, class FF>

double jkqtpstatModifiedSum	(	InputIt	first,
		InputIt	last,
		FF	modifierFunctor,
		size_t *	Noutput = nullptr )

inline

calculates the sum of a given data range first ... last of values, modifying each value with a given functor modifierFunctor before accumulating

Template Parameters

InputIt	standard iterator type of first and last.
FF	a functor type

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	modifierFunctor	the function to apply to each element in the range before summation (of type FF )
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: Sum of modified data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sum(X)=\cdot\sum\limits_{i=1}^{N}\mbox{modifierFunctor}(X_i)$

This function allows to e.g. calculate the sum of squares by calling

jkqtpstatModifiedSum(first, last, [](double v) { return v*v; });

jkqtpstatModifiedSum(first, last, &jkqtp_sqr<double>);

jkqtp_sqr

T jkqtp_sqr(const T &v)

returns the quare of the value v, i.e. v*v

Definition jkqtpmathtools.h:327

jkqtpstatModifiedSum

double jkqtpstatModifiedSum(InputIt first, InputIt last, FF modifierFunctor, size_t *Noutput=nullptr)

calculates the sum of a given data range first ... last of values, modifying each value with a given ...

Definition jkqtpstatbasics.h:320

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatMoment()

template<class InputIt>

double jkqtpstatMoment	(	InputIt	first,
		InputIt	last,
		int	order,
		size_t *	Noutput = nullptr )

inline

calculates the given (non-central) moment $\langle X^o\rangle$ of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	order	oder of the central moment $\langle X^o\rangle$
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the given moment $\langle X^o\rangle$ of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\langle X^n\rangle= \mathbb{E}\left[X^n\right]$

where $\mu$ is the mean of a random variable and $\overline{x}$ is the average (calculated using jkqtpstatAverage() ) of the input dataset .

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatNMAD()

template<class InputIt>

double jkqtpstatNMAD	(	InputIt	first,
		InputIt	last,
		double *	median = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the normalized median absolute deviation about the median (NMAD) of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	median	optionally returns the median value in this variable
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the normalized median absolute deviation about the median (NMAD) of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

This function calculates

$\mbox{NMAD}(\vec{x})=\frac{\mbox{MAD}(\vec{x})}{0.6745}=\frac{\mbox{Med}\left\{|\vec{x}-\mbox{Med}(\vec{x})|\right\}}{0.6745}$

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

See also: https://en.wikipedia.org/wiki/Median_absolute_deviation and Ricardo A. Maronna, R. Douglas Martin, Victor J. Yohai: "Robust Statistics: Theory and Methods", Wiley, 2006, ISBN: 978-0-470-01092-1

◆ jkqtpstatQuantile()

template<class InputIt>

double jkqtpstatQuantile	(	InputIt	first,
		InputIt	last,
		double	quantile,
		size_t *	Noutput = nullptr )

inline

calculates the quantile -th quantile of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	quantile	the given quantile, range 0..1 (e.g. 0.25 for the 25% quartile ...)
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: the quantile -th quantile of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

Note: This operation implies an internal copy of the data, as well as sorting it!; Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatSkewness()

template<class InputIt>

double jkqtpstatSkewness	(	InputIt	first,
		InputIt	last,
		double *	averageOut = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the skewness $\gamma_1=\mathbb{E}\left[\left(\frac{X-\mu}{\sigma}\right)^3\right]$ of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	averageOut	returns (optionally) the average of the dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: skewness $\gamma_1$ of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\gamma_1=\mathbb{E}\left[\left(\frac{X-\mu}{\sigma}\right)^3\right]= \frac{m_3}{m_2^{3/2}} = \frac{\frac{1}{n} \sum_{i=1}^n (x_i-\overline{x})^3}{\left(\frac{1}{n} \sum_{i=1}^n (x_i-\overline{x})^2\right)^{3/2}}$

where $\mu$ is the mean and $\sigma$ the standard deviation of a random variable and $\overline{x}$ is the average (calculated using jkqtpstatAverage() ) of the input dataset .

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatStdDev()

template<class InputIt>

double jkqtpstatStdDev	(	InputIt	first,
		InputIt	last,
		double *	averageOut = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the standard deviation $\sigma_X=\sqrt{\mbox{Var}(X)}$ of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	averageOut	returns (optionally) the average of the dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: standard deviation of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sigma_X=\sqrt{\frac{1}{N-1}\cdot\sum\limits_{i=1}^{N}(X_i-\overline{X})^2}=$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatSum()

template<class InputIt>

double jkqtpstatSum	(	InputIt	first,
		InputIt	last,
		size_t *	Noutput = nullptr )

inline

calculates the sum of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: Sum of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sum(X)=\cdot\sum\limits_{i=1}^{N}X_i$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatSumSqr()

template<class InputIt>

double jkqtpstatSumSqr	(	InputIt	first,
		InputIt	last,
		size_t *	Noutput = nullptr )

inline

calculates the sum of squares of a given data range first ... last

Template Parameters

InputIt standard iterator type of first and last.

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: Sum of squares of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sum(X)=\cdot\sum\limits_{i=1}^{N}X_i^2$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatVariance()

template<class InputIt>

double jkqtpstatVariance	(	InputIt	first,
		InputIt	last,
		double *	averageOut = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the variance $\sigma_X^2=\mbox{Var}(X)$ of a given data range first ... last

Template Parameters

InputIt	standard iterator type of first and last.
InputWeightIt	standard iterator type of firstWeight

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
[out]	averageOut	returns (optionally) the average of the dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: Variance of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sigma_X^2=\text{Var}(X)=\frac{1}{N-1}\cdot\sum\limits_{i=1}^{N}(X_i-\overline{X})^2=\frac{1}{N-1}\cdot\left(\sum_{i=1}^NX_i^2-\frac{1}{N}\cdot\left(\sum_{i=1}^NX_i\right)^2\right)$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatWeightedAverage()

template<class InputIt, class InputWeightIt>

double jkqtpstatWeightedAverage	(	InputIt	first,
		InputIt	last,
		InputWeightIt	firstWeight,
		size_t *	Noutput = nullptr )

inline

calculates the weighted average of a given data range first ... last

Template Parameters

InputIt	standard iterator type of first and last.
InputWeightIt	standard iterator type of firstWeight

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	firstWeight	iterator pointing to the first item in the weights dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: weighted average of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, NAN is returned

This function implements:

$\overline{X}=\frac{\sum\limits_{i=1}^{N}w_i\cdot X_i}{\sum\limits_{i=1}^{N}w_i}$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatWeightedStdDev()

template<class InputIt, class InputWeightIt>

double jkqtpstatWeightedStdDev	(	InputIt	first,
		InputIt	last,
		InputWeightIt	firstWeight,
		double *	averageOut = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the weighted standard deviation $\sigma_X=\sqrt{\mbox{Var}(X)}$ of a given data range first ... last

Template Parameters

InputIt	standard iterator type of first and last.
InputWeightIt	standard iterator type of firstWeight

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	firstWeight	iterator pointing to the first item in the weights dataset
[out]	averageOut	returns (optionally) the average of the dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: weighted standard deviation of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sigma_v=\sqrt{\frac{\sum\limits_{i=1}^{N}w_i\cdot (v_i-\overline{v})^2}{\sum\limits_{i=1}^{N}w_i}}$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

◆ jkqtpstatWeightedVariance()

template<class InputIt, class InputWeightIt>

double jkqtpstatWeightedVariance	(	InputIt	first,
		InputIt	last,
		InputWeightIt	firstWeight,
		double *	averageOut = nullptr,
		size_t *	Noutput = nullptr )

inline

calculates the weighted variance $\sigma_X^2=\mbox{Var}(X)$ of a given data range first ... last

Template Parameters

InputIt	standard iterator type of first and last.
InputWeightIt	standard iterator type of firstWeight

Parameters

	first	iterator pointing to the first item in the dataset to use
	last	iterator pointing behind the last item in the dataset to use
	firstWeight	iterator pointing to the first item in the weights dataset
[out]	averageOut	returns (optionally) the average of the dataset
[out]	Noutput	optionally returns the number of accumulated valid values in this variable

Returns: weighted standard deviation of the data returned between first and last (excluding invalid doubles). If the given range first ... last is empty, 0 is returned

This function implements:

$\sigma_v^2=\text{Var}(v)=\frac{\sum\limits_{i=1}^{N}w_i\cdot (v_i-\overline{v})^2}{\sum\limits_{i=1}^{N}w_i}$

Note: Each value is the specified range is converted to a double using jkqtp_todouble(). Entries in the range that are invalid double (using JKQTPIsOKFloat() ) are ignored when calculating.

Classes

Functions

Detailed Description

Function Documentation

◆ jkqtpstat5NumberStatistics() [1/2]

◆ jkqtpstat5NumberStatistics() [2/2]

◆ jkqtpstat5NumberStatisticsAndOutliers()

◆ jkqtpstat5NumberStatisticsAndOutliersOfSortedVector()

◆ jkqtpstat5NumberStatisticsOfSortedVector()

◆ jkqtpstatAverage()

◆ jkqtpstatCentralMoment()

◆ jkqtpstatCorrelationCoefficient()

◆ jkqtpstatCount()

◆ jkqtpstatCumSum()

◆ jkqtpstatFilterGoodFloat()

◆ jkqtpstatMAD()

◆ jkqtpstatMaximum()

◆ jkqtpstatMedian()

◆ jkqtpstatMedianAndPartialSort()

◆ jkqtpstatMedianOfSortedVector()

◆ jkqtpstatMinimum()

◆ jkqtpstatMinMax()

◆ jkqtpstatModifiedSum()

◆ jkqtpstatMoment()

◆ jkqtpstatNMAD()

◆ jkqtpstatQuantile()

◆ jkqtpstatSkewness()

◆ jkqtpstatStdDev()

◆ jkqtpstatSum()

◆ jkqtpstatSumSqr()

◆ jkqtpstatVariance()

◆ jkqtpstatWeightedAverage()

◆ jkqtpstatWeightedStdDev()

◆ jkqtpstatWeightedVariance()