JKQTPlotter trunk/v5.0.0
an extensive Qt5+Qt6 Plotter framework (including a feature-richt plotter widget, a speed-optimized, but limited variant and a LaTeX equation renderer!), written fully in C/C++ and without external dependencies
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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 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 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 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 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 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 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 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 of a given data range first ... last | |
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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)
InputIt | standard iterator type of first and last. |
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
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[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
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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)
InputIt | standard iterator type of first and last. |
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!) |
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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)
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 |
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
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[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
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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
TVector | a type, compatible with std::vector (i,e, providing size(), []-element access and iterators) |
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
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[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
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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
TVector | a type, compatible with std::vector (i,e, providing size(), []-element access and iterators) |
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
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[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
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calculates the average of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function implements:
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calculates the given central moment of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 | |
[out] | averageOut | returns (optionally) the average of the dataset |
[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
This function implements:
where is the mean of a random variable and is the average (calculated using jkqtpstatAverage() ) of the input dataset .
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calculate empirical (Pearson's) correlation coefficient between two given data ranges first1 ... last1 and first2 ... last2
InputIt1 | standard iterator type of first1 and last1. |
InputIt2 | standard iterator type of first2 and last2. |
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 |
This function implements:
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calculates the number of valid values in the given data range first ... last
InputIt | standard iterator type of first and last. |
first | iterator pointing to the first item in the dataset to use |
last | iterator pointing behind the last item in the dataset to use |
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calculates the vector of cummulative (or partial) sums of a given data range first ... last
InputIt | standard iterator type of first and last. |
OutputIt | standard output iterator type |
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:
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filters the given data range first ... last for good floats (using JKQTPIsOKFloat() )
InputIt | standard iterator type of first and last. |
OutputIt | standard output iterator type |
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 |
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calculates the median absolute deviation about the median (MAD) of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function calculates
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calculates the maximum value in the given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
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calculates the median of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
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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!)
InputIt | standard iterator type of first and last. |
first | iterator pointing to the first item in the dataset to use |
last | iterator pointing behind the last item in the dataset to use |
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calculates the median of a given sorted (!) data vector
TVector | a type, compatible with std::vector (i,e, providing size(), []-element access and iterators) |
data | a sorted vector with values | |
[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
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calculates the minimum value in the given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
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calculates the minimum and maximum values in the given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
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calculates the sum of a given data range first ... last of values, modifying each value with a given functor modifierFunctor before accumulating
InputIt | standard iterator type of first and last. |
FF | a functor type |
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 |
This function implements:
This function allows to e.g. calculate the sum of squares by calling
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calculates the given (non-central) moment of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 | |
[out] | Noutput | optionally returns the number of accumulated valid values in this variable |
This function implements:
where is the mean of a random variable and is the average (calculated using jkqtpstatAverage() ) of the input dataset .
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calculates the normalized median absolute deviation about the median (NMAD) of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function calculates
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calculates the quantile -th quantile of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
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calculates the skewness of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function implements:
where is the mean and the standard deviation of a random variable and is the average (calculated using jkqtpstatAverage() ) of the input dataset .
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calculates the standard deviation of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function implements:
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calculates the sum of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function implements:
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calculates the sum of squares of a given data range first ... last
InputIt | standard iterator type of first and last. |
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 |
This function implements:
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calculates the variance of a given data range first ... last
InputIt | standard iterator type of first and last. |
InputWeightIt | standard iterator type of firstWeight |
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 |
This function implements:
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calculates the weighted average of a given data range first ... last
InputIt | standard iterator type of first and last. |
InputWeightIt | standard iterator type of firstWeight |
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 |
This function implements:
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calculates the weighted standard deviation of a given data range first ... last
InputIt | standard iterator type of first and last. |
InputWeightIt | standard iterator type of firstWeight |
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 |
This function implements:
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calculates the weighted variance of a given data range first ... last
InputIt | standard iterator type of first and last. |
InputWeightIt | standard iterator type of firstWeight |
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 |
This function implements: