A class providing methods for descriptive statistics. More...

#include <describe.hpp>

Public Member Functions
double	mean_geo (const std::vector< double > &data)
	Calculates the geometric mean of a given dataset. More...

double	mean_cubic (const std::vector< double > &data, double p)
	Calculates the cubic generalized mean of a given dataset with a specified power. More...

double	mean_geo_pow (const std::vector< double > &data, double p)
	Calculates the power geometric mean of a given dataset with a specified power. More...

double	mean_harmonic (const std::vector< double > &data)
	Calculates the harmonic mean of a given dataset. More...

double	mean_heronian (const std::vector< double > &data)
	Calculates the Heronian mean of a given dataset. More...

double	mean_heinz (const std::vector< double > &data)
	Calculates the Heinz mean of a given dataset. More...

double	mean_lehmer (const std::vector< double > &data, double p)
	Calculates the Lehmer mean of a given dataset with a specified power. More...

double	Median (std::vector< double > data)
	Calculates the median of a given dataset. More...

double	avg_abs_dev (const std::vector< double > &data)
	Calculates the average absolute deviation of a given dataset. More...

double	var_coeff (const std::vector< double > &data)
	Calculates the coefficient of variation of a given dataset. More...

double	iq_range (const std::vector< double > &data)
	Calculates the interquartile range of a given dataset. More...

double	percentile (const std::vector< double > &data, double percentile)
	Calculates the specified percentile of a given dataset. More...

double	range (const std::vector< double > &data)
	Calculates the range of a given dataset. More...

double	clt (const std::vector< double > &data, int numSamples)
	Calculates the standard error of the mean using the Central Limit Theorem. More...

double	kurtosis (const std::vector< double > &data, double mean)
	Calculates the kurtosis of a given dataset. More...

double	lmoment1 (const std::vector< double > &data, double mean)
	Calculates the first L-moment of a given dataset. More...

double	lmoment2 (const std::vector< double > &data, double mean)
	Calculates the second L-moment of a given dataset. More...

double	skewness (const std::vector< double > &data, double mean, double stddev)
	Calculates the skewness of a given dataset. More...

std::vector< size_t >	rank_data (const std::vector< double > &data)
	Ranks the data in ascending order. More...

double	partial_corr (const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &z)
	Calculates the partial correlation coefficient between two variables, controlling for a third variable. More...

double	ppmc (const std::vector< double > &x, const std::vector< double > &y)
	Calculates the Pearson Product-Moment Correlation between two variables. More...

double	kendalls_tau (const std::vector< double > &x, const std::vector< double > &y)
	Calculates Kendall's Tau Rank Correlation between two variables. More...

double	spearmans_rho (const std::vector< double > &x, const std::vector< double > &y)
	Calculates Spearman's Rank Correlation between two variables. More...

Static Public Member Functions
static double	u_stat (const std::vector< double > &sample1, const std::vector< double > &sample2)
	Calculates U statistic given two samples. More...

static double	mean_arith (const std::vector< double > &data)
	Calculates the arithmetic mean of a given dataset. More...

static double	stdev (const std::vector< double > &data, double mean)
	Calculates the standard deviation of a given dataset, given the mean. More...

static double	variance (const std::vector< double > &data, double mean)
	Calculates the variance of a given dataset, given the mean. More...

Detailed Description

A class providing methods for descriptive statistics.

Definition at line 44 of file describe.hpp.

Member Function Documentation

◆ avg_abs_dev()

double gpmp::stats::Describe::avg_abs_dev ( const std::vector< double > & data )

Calculates the average absolute deviation of a given dataset.

Parameters

data	The input dataset

Returns: The average absolute deviation

Definition at line 138 of file describe.cpp.

                                                                    {
     double mean = mean_arith(data);
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::abs(value - mean);
     }
     return sum / static_cast<double>(data.size());
 }

◆ clt()

double gpmp::stats::Describe::clt	(	const std::vector< double > &	data,
		int	numSamples
	)

Calculates the standard error of the mean using the Central Limit Theorem.

This method estimates the standard error of the mean based on the Central Limit Theorem

Parameters

data	The input dataset
numSamples	The number of samples for the Central Limit Theorem

Returns: The estimated standard error of the mean

Definition at line 204 of file describe.cpp.

                                                   {
     double mean = mean_arith(data);
     double stddev = stdev(data, mean);
     return stddev / std::sqrt(static_cast<double>(numSamples));
 }

◆ iq_range()

double gpmp::stats::Describe::iq_range ( const std::vector< double > & data )

Calculates the interquartile range of a given dataset.

Parameters

data	The input dataset

Returns: The interquartile range

Definition at line 155 of file describe.cpp.

                                                                 {
     std::vector<double> sortedData = data;
     std::sort(sortedData.begin(), sortedData.end());
  
     size_t size = sortedData.size();
     size_t lowerIndex = size / 4;
     size_t upperIndex = 3 * size / 4;
  
     return sortedData[upperIndex] - sortedData[lowerIndex];
 }

◆ kendalls_tau()

double gpmp::stats::Describe::kendalls_tau	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Calculates Kendall's Tau Rank Correlation between two variables.

This method measures the strength and direction of monotonic relationships between variables X and Y

Parameters

x	The values of variable X
y	The values of variable Y

Returns: Kendall's Tau Rank Correlation coefficient

Definition at line 300 of file describe.cpp.

                                                                        {
     size_t concordant = 0;
     size_t discordant = 0;
  
     for (size_t i = 0; i < x.size() - 1; ++i) {
         for (size_t j = i + 1; j < x.size(); ++j) {
             if ((x[i] < x[j] && y[i] < y[j]) || (x[i] > x[j] && y[i] > y[j])) {
                 concordant++;
             } else if ((x[i] < x[j] && y[i] > y[j]) ||
                        (x[i] > x[j] && y[i] < y[j])) {
                 discordant++;
             }
         }
     }
  
     return static_cast<double>(concordant - discordant) /
            std::sqrt(static_cast<double>((concordant + discordant) *
                                          (x.size() * (x.size() - 1)) / 2));
 }

◆ kurtosis()

double gpmp::stats::Describe::kurtosis	(	const std::vector< double > &	data,
		double	mean
	)

Calculates the kurtosis of a given dataset.

This method measures the "tailedness" or sharpness of the dataset's peak

Parameters

data	The input dataset
mean	The mean of the dataset

Returns: The kurtosis value

Definition at line 212 of file describe.cpp.

                                                     {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value - mean, 4.0);
     }
     double var = variance(data, mean);
     return sum / (data.size() * std::pow(var, 2.0)) - 3.0;
 }

◆ lmoment1()

double gpmp::stats::Describe::lmoment1	(	const std::vector< double > &	data,
		double	mean
	)

Calculates the first L-moment of a given dataset.

L-moments are used to estimate the parameters of a probability distribution

Parameters

data	The input dataset
mean	The mean of the dataset

Returns: The first L-moment

Definition at line 223 of file describe.cpp.

                                                     {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value - mean, 3.0);
     }
     return sum / data.size();
 }

◆ lmoment2()

double gpmp::stats::Describe::lmoment2	(	const std::vector< double > &	data,
		double	mean
	)

Calculates the second L-moment of a given dataset.

L-moments are used to estimate the parameters of a probability distribution

Parameters

data	The input dataset
mean	The mean of the dataset

Returns: The second L-moment

Definition at line 232 of file describe.cpp.

                                                     {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value - mean, 4.0);
     }
     return sum / data.size();
 }

◆ mean_arith()

double gpmp::stats::Describe::mean_arith ( const std::vector< double > & data )

static

Calculates the arithmetic mean of a given dataset.

Parameters

data	The input dataset

Returns: The arithmetic mean

Definition at line 52 of file describe.cpp.

                                                                   {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += value;
     }
     return sum / static_cast<double>(data.size());
 }

Referenced by gpmp::stats::HypothesisTest::ANOVA(), gpmp::stats::ProbDist::ConfidenceInterval(), gpmp::stats::ProbDist::mom(), gpmp::stats::HypothesisTest::one_sample_ttest(), gpmp::stats::ProbDist::PivotFunctionForConfidenceInterval(), and gpmp::stats::HypothesisTest::two_sample_ttest().

◆ mean_cubic()

double gpmp::stats::Describe::mean_cubic	(	const std::vector< double > &	data,
		double	p
	)

Calculates the cubic generalized mean of a given dataset with a specified power.

Parameters

data	The input dataset
p	The power parameter

Returns: The cubic generalized mean

Definition at line 70 of file describe.cpp.

                                                    {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value, p);
     }
     return std::pow(sum / static_cast<double>(data.size()), 1.0 / p);
 }

◆ mean_geo()

double gpmp::stats::Describe::mean_geo ( const std::vector< double > & data )

Calculates the geometric mean of a given dataset.

Parameters

data	The input dataset

Returns: The geometric mean

Definition at line 61 of file describe.cpp.

                                                                 {
     double product = 1.0;
     for (const auto &value : data) {
         product *= value;
     }
     return std::pow(product, 1.0 / static_cast<double>(data.size()));
 }

◆ mean_geo_pow()

double gpmp::stats::Describe::mean_geo_pow	(	const std::vector< double > &	data,
		double	p
	)

Calculates the power geometric mean of a given dataset with a specified power.

Parameters

data	The input dataset
p	The power parameter

Returns: The power geometric mean

Definition at line 80 of file describe.cpp.

                                                      {
     double product = 1.0;
     for (const auto &value : data) {
         product *= std::pow(value, p);
     }
     return std::pow(product, 1.0 / static_cast<double>(data.size()));
 }

◆ mean_harmonic()

double gpmp::stats::Describe::mean_harmonic ( const std::vector< double > & data )

Calculates the harmonic mean of a given dataset.

Parameters

data	The input dataset

Returns: The harmonic mean

Definition at line 90 of file describe.cpp.

                                                                      {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += 1.0 / value;
     }
     return static_cast<double>(data.size()) / sum;
 }

◆ mean_heinz()

double gpmp::stats::Describe::mean_heinz ( const std::vector< double > & data )

Calculates the Heinz mean of a given dataset.

Parameters

data	The input dataset

Returns: The Heinz mean

Definition at line 108 of file describe.cpp.

                                                                   {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += value * std::log(value);
     }
     return std::exp(sum / static_cast<double>(data.size()));
 }

◆ mean_heronian()

double gpmp::stats::Describe::mean_heronian ( const std::vector< double > & data )

Calculates the Heronian mean of a given dataset.

Parameters

data	The input dataset

Returns: The Heronian mean

Definition at line 99 of file describe.cpp.

                                                                      {
     double product = 1.0;
     for (const auto &value : data) {
         product *= std::sqrt(value);
     }
     return std::pow(product, 2.0 / static_cast<double>(data.size()));
 }

◆ mean_lehmer()

double gpmp::stats::Describe::mean_lehmer	(	const std::vector< double > &	data,
		double	p
	)

Calculates the Lehmer mean of a given dataset with a specified power.

Parameters

data	The input dataset
p	The power parameter

Returns: The Lehmer mean

Definition at line 117 of file describe.cpp.

                                                     {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value, p);
     }
     return sum / static_cast<double>(data.size());
 }

◆ Median()

double gpmp::stats::Describe::Median ( std::vector< double > data )

Calculates the median of a given dataset.

Parameters

data	The input dataset

Returns: The median

Definition at line 127 of file describe.cpp.

                                                        {
     std::sort(data.begin(), data.end());
     size_t size = data.size();
     if (size % 2 == 0) {
         return (data[size / 2 - 1] + data[size / 2]) / 2.0;
     } else {
         return data[size / 2];
     }
 }

◆ partial_corr()

double gpmp::stats::Describe::partial_corr	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const std::vector< double > &	z
	)

Calculates the partial correlation coefficient between two variables, controlling for a third variable.

This method computes the partial correlation between variables X and Y, controlling for variable Z

Parameters

x	The values of variable X
y	The values of variable Y
z	The values of control variable Z

Returns: The partial correlation coefficient

Definition at line 269 of file describe.cpp.

                                                                        {
     double r_xy = ppmc(x, y);
     double r_xz = ppmc(x, z);
     double r_yz = ppmc(y, z);
  
     return (r_xy - (r_xz * r_yz)) /
            std::sqrt((1.0 - std::pow(r_xz, 2.0)) * (1.0 - std::pow(r_yz, 2.0)));
 }

◆ percentile()

double gpmp::stats::Describe::percentile	(	const std::vector< double > &	data,
		double	percentile
	)

Calculates the specified percentile of a given dataset.

Parameters

data	The input dataset
percentile	The desired percentile (00 to 10)

Returns: The value at the specified percentile

Definition at line 167 of file describe.cpp.

                                                             {
     std::vector<double> sortedData = data;
     std::sort(sortedData.begin(), sortedData.end());
  
     size_t size = sortedData.size();
     size_t index = static_cast<size_t>(percentile * (size - 1));
     return sortedData[index];
 }

◆ ppmc()

double gpmp::stats::Describe::ppmc	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Calculates the Pearson Product-Moment Correlation between two variables.

This method measures the linear relationship between variables X and Y

Parameters

x	The values of variable X
y	The values of variable Y

Returns: The Pearson Product-Moment Correlation coefficient

Definition at line 281 of file describe.cpp.

                                                                {
     double mean_x = mean_arith(x);
     double mean_y = mean_arith(y);
  
     double numerator = 0.0;
     double denominator_x = 0.0;
     double denominator_y = 0.0;
  
     for (size_t i = 0; i < x.size(); ++i) {
         numerator += (x[i] - mean_x) * (y[i] - mean_y);
         denominator_x += std::pow(x[i] - mean_x, 2.0);
         denominator_y += std::pow(y[i] - mean_y, 2.0);
     }
  
     return numerator / std::sqrt(denominator_x * denominator_y);
 }

◆ range()

double gpmp::stats::Describe::range ( const std::vector< double > & data )

Calculates the range of a given dataset.

Parameters

data	The input dataset

Returns: The range

Definition at line 178 of file describe.cpp.

                                                              {
     auto result = std::minmax_element(data.begin(), data.end());
     return *result.second - *result.first;
 }

◆ rank_data()

std::vector< size_t > gpmp::stats::Describe::rank_data ( const std::vector< double > & data )

Ranks the data in ascending order.

This method assigns ranks to the data, where the smallest value gets rank 1, the second smallest gets rank 2, and so on

Parameters

data	The input dataset

Returns: A vector containing the ranks of the input data

Definition at line 253 of file describe.cpp.

                                                           {
     std::vector<size_t> ranks(data.size());
  
     for (size_t i = 0; i < data.size(); ++i) {
         size_t rank = 1;
         for (size_t j = 0; j < data.size(); ++j) {
             if (j != i && data[j] < data[i]) {
                 rank++;
             }
         }
         ranks[i] = rank;
     }
  
     return ranks;
 }

◆ skewness()

double gpmp::stats::Describe::skewness	(	const std::vector< double > &	data,
		double	mean,
		double	stddev
	)

Calculates the skewness of a given dataset.

This method measures the asymmetry of the dataset's distribution

Parameters

data	The input dataset
mean	The mean of the dataset
stddev	The standard deviation of the dataset

Returns: The skewness value

Definition at line 242 of file describe.cpp.

                                                       {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow((value - mean) / stddev, 3.0);
     }
     return sum / static_cast<double>(data.size());
 }

◆ spearmans_rho()

double gpmp::stats::Describe::spearmans_rho	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Calculates Spearman's Rank Correlation between two variables.

This method measures the strength and direction of monotonic relationships between variables X and Y

Parameters

x	The values of variable X
y	The values of variable Y

Returns: Spearman's Rank Correlation coefficient

Definition at line 322 of file describe.cpp.

                                                                         {
     std::vector<size_t> ranks_x = rank_data(x);
     std::vector<size_t> ranks_y = rank_data(y);
  
     double d_squared = 0.0;
     for (size_t i = 0; i < x.size(); ++i) {
         d_squared += std::pow(ranks_x[i] - ranks_y[i], 2.0);
     }
  
     return 1.0 -
            (6.0 * d_squared) / (x.size() * (std::pow(x.size(), 2.0) - 1.0));
 }

◆ stdev()

double gpmp::stats::Describe::stdev	(	const std::vector< double > &	data,
		double	mean
	)

static

Calculates the standard deviation of a given dataset, given the mean.

Parameters

data	The input dataset
mean	The mean of the dataset

Returns: The standard deviation

Definition at line 184 of file describe.cpp.

                                                  {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value - mean, 2.0);
     }
     return std::sqrt(sum / static_cast<double>(data.size()));
 }

Referenced by gpmp::stats::ProbDist::ConfidenceInterval(), gpmp::stats::HypothesisTest::one_sample_ttest(), and gpmp::stats::ProbDist::PivotFunctionForConfidenceInterval().

◆ u_stat()

double gpmp::stats::Describe::u_stat	(	const std::vector< double > &	sample1,
		const std::vector< double > &	sample2
	)

static

Calculates U statistic given two samples.

Parameters

sample1
sample2

Returns: U statistic

Definition at line 38 of file describe.cpp.

                                                                        {
     double U = 0;
     for (double x1 : sample1) {
         for (double x2 : sample2) {
             if (x1 < x2) {
                 U++;
             }
         }
     }
     return U;
 }

Referenced by gpmp::stats::HypothesisTest::mann_whitney_test().

◆ var_coeff()

double gpmp::stats::Describe::var_coeff ( const std::vector< double > & data )

Calculates the coefficient of variation of a given dataset.

Parameters

data	The input dataset

Returns: The coefficient of variation (in percentage)

Definition at line 148 of file describe.cpp.

                                                                  {
     double mean = mean_arith(data);
     double stddev = stdev(data, mean);
     return (stddev / mean) * 100.0; // Multiply by 100 for percentage
 }

◆ variance()

double gpmp::stats::Describe::variance	(	const std::vector< double > &	data,
		double	mean
	)

static

Calculates the variance of a given dataset, given the mean.

Parameters

data	The input dataset
mean	The mean of the dataset

Returns: The variance

Definition at line 194 of file describe.cpp.

                                                     {
     double sum = 0.0;
     for (const auto &value : data) {
         sum += std::pow(value - mean, 2.0);
     }
     return sum / static_cast<double>(data.size());
 }

Referenced by gpmp::stats::ProbDist::mom(), and gpmp::stats::HypothesisTest::two_sample_ttest().

The documentation for this class was generated from the following files:

include/openGPMP/stats/describe.hpp
modules/stats/describe.cpp

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ avg_abs_dev()

◆ clt()

◆ iq_range()

◆ kendalls_tau()

◆ kurtosis()

◆ lmoment1()

◆ lmoment2()

◆ mean_arith()

◆ mean_cubic()

◆ mean_geo()

◆ mean_geo_pow()

◆ mean_harmonic()

◆ mean_heinz()

◆ mean_heronian()

◆ mean_lehmer()

◆ Median()

◆ partial_corr()

◆ percentile()

◆ ppmc()

◆ range()

◆ rank_data()

◆ skewness()

◆ spearmans_rho()

◆ stdev()

◆ u_stat()

◆ var_coeff()

◆ variance()