#include <probdist.hpp>

Public Member Functions
double	quantile_dist (double probability)
	Compute the quantile of the standard normal distribution. More...

double	normal_PDF (double x, double mean, double stddev)
	Compute the probability density function (PDF) for the normal distribution. More...

double	normal_CDF (double x, double mean, double stddev)
	Compute the cumulative distribution function (CDF) for the normal distribution. More...

double	uniform_CDF (size_t k, size_t n)
	Compute the cumulative distribution function (CDF) for the uniform distribution. More...

double	exp_PDF (double x, size_t k, double lambda)
	Compute the probability density function (PDF) for the exponential distribution. More...

double	emp_CDF (const std::vector< double > &data, double x)
	Compute the empirical cumulative distribution function (CDF) for a given value. More...

double	emp_PMF (const std::vector< double > &data, double x)
	Compute the empirical probability mass function (PMF) for a given value. More...

double	inverse_emp_CDF (const std::vector< double > &data, double p)
	Compute the inverse of the empirical cumulative distribution function (CDF) for a given probability. More...

double	mle (const std::vector< double > &data)
	Compute the Maximum Likelihood Estimate (MLE) for the mean of a dataset. More...

double	mom (const std::vector< double > &data)
	Compute the method of moments (MOM) estimate for the mean of a dataset. More...

double	mle_est (const std::vector< double > &data)
	Placeholder function for M-estimation. More...

double	mumv (const std::vector< double > &data)
	Compute the Mean-Unbiased Minimum-Variance (MUMV) estimate for the mean of a dataset. More...

double	median_uniased (const std::vector< double > &data)
	Compute the median-unbiased estimate for the median of a dataset. More...

std::pair< double, double >	ConfidenceInterval (const std::vector< double > &data, double alpha)
	Compute the confidence interval for the mean of a dataset. More...

double	Pivot (const std::vector< double > &data, double pivotFunction(const std::vector< double > &))
	Compute the value of a pivot function for interval estimation. More...

double	PivotFunctionForConfidenceInterval (const std::vector< double > &data)
	Example pivot function for computing a confidence interval. More...

std::pair< double, double >	LikelihoodInterval (const std::vector< double > &data, double alpha)
	Compute the likelihood interval for a given dataset and significance level. More...

std::pair< double, double >	PredictionInterval (const std::vector< double > &data, double alpha)
	Compute the prediction interval for a given dataset and significance level. More...

std::pair< double, double >	ToleranceInterval (const std::vector< double > &data, double alpha)
	Compute the tolerance interval for a given dataset and significance level. More...

Detailed Description

Definition at line 42 of file probdist.hpp.

Member Function Documentation

◆ ConfidenceInterval()

std::pair< double, double > gpmp::stats::ProbDist::ConfidenceInterval	(	const std::vector< double > &	data,
		double	alpha
	)

Compute the confidence interval for the mean of a dataset.

Parameters

data	The dataset
alpha	The confidence level

Returns: A pair representing the lower and upper bounds of the confidence interval

Definition at line 253 of file probdist.cpp.

                                                         {
     if (data.empty() || alpha <= 0.0 || alpha >= 1.0) {
         return {0.0, 0.0}; // Invalid input, return an empty interval
     }
  
     size_t n = data.size();
     gpmp::stats::Describe desc;
     double mean = desc.mean_arith(data);
     double stddev = desc.stdev(data, mean);
  
     // Assuming a normal distribution for simplicity
     double z = quantile_dist(1 - alpha / 2.0);
     double margin = z * stddev / std::sqrt(static_cast<double>(n));
  
     return {mean - margin, mean + margin};
 }

References gpmp::stats::Describe::mean_arith(), and gpmp::stats::Describe::stdev().

◆ emp_CDF()

double gpmp::stats::ProbDist::emp_CDF	(	const std::vector< double > &	data,
		double	x
	)

Compute the empirical cumulative distribution function (CDF) for a given value.

Parameters

data	The dataset
x	The value at which to evaluate the empirical CDF

Returns: The empirical CDF value at the given point

Definition at line 168 of file probdist.cpp.

                                                 {
     size_t count = 0;
     for (const auto &value : data) {
         if (value <= x) {
             count++;
         }
     }
  
     return static_cast<double>(count) / data.size();
 }

◆ emp_PMF()

double gpmp::stats::ProbDist::emp_PMF	(	const std::vector< double > &	data,
		double	x
	)

Compute the empirical probability mass function (PMF) for a given value.

Parameters

data	The dataset
x	The value at which to evaluate the empirical PMF

Returns: The empirical PMF value at the given point

Definition at line 180 of file probdist.cpp.

                                                 {
     size_t count = std::count(data.begin(), data.end(), x);
     return static_cast<double>(count) / data.size();
 }

◆ exp_PDF()

double gpmp::stats::ProbDist::exp_PDF	(	double	x,
		size_t	k,
		double	lambda
	)

Compute the probability density function (PDF) for the exponential distribution.

Parameters

x	The value at which to evaluate the PDF
k	The shape parameter of the distribution
lambda	The rate parameter of the distribution

Returns: The PDF value at the given point

Definition at line 150 of file probdist.cpp.

                                                                    {
     // Check if k is valid (k must be 1 for exponential distribution)
     if (k != 1) {
         // Return 0 if k is not 1, as exponential distribution is only defined
         // for k = 1
         return 0.0;
     }
  
     // Check if lambda is non-positive
     if (lambda <= 0) {
         // Return 0 if lambda is non-positive
         return 0.0;
     }
  
     // Calculate the exponential PDF
     return (k / lambda) * exp(-k * x);
 }

◆ inverse_emp_CDF()

double gpmp::stats::ProbDist::inverse_emp_CDF	(	const std::vector< double > &	data,
		double	p
	)

Compute the inverse of the empirical cumulative distribution function (CDF) for a given probability.

Parameters

data	The dataset
p	The probability value between 0 and 1

Returns: The value at which the empirical CDF is equal to or greater than the given probability

Definition at line 186 of file probdist.cpp.

                                                         {
     if (data.empty() || p < 0.0 || p > 1.0) {
         return 0.0; // Invalid input, return 0
     }
  
     std::vector<double> sortedData = data;
     std::sort(sortedData.begin(), sortedData.end());
  
     size_t index = static_cast<size_t>(p * (data.size() - 1));
     return sortedData[index];
 }

◆ LikelihoodInterval()

std::pair< double, double > gpmp::stats::ProbDist::LikelihoodInterval	(	const std::vector< double > &	data,
		double	alpha
	)

Compute the likelihood interval for a given dataset and significance level.

Parameters

data	The dataset
alpha	The significance level

Returns: A pair representing the lower and upper bounds of the likelihood interval

Definition at line 294 of file probdist.cpp.

                                                         {
     // Example implementation, this needs to be adapted based on the specific
     // likelihood function
     if (data.empty() || alpha <= 0.0 || alpha >= 1.0) {
         return {0.0, 0.0}; // Invalid input, return an empty interval
     }
  
     // Placeholder, implement likelihood function and find confidence bounds
     double lowerBound = 0.0;
     double upperBound = 1.0;
  
     return {lowerBound, upperBound};
 }

◆ median_uniased()

double gpmp::stats::ProbDist::median_uniased ( const std::vector< double > & data )

Compute the median-unbiased estimate for the median of a dataset.

Parameters

data	The dataset

Returns: The median-unbiased estimate for the median

Definition at line 235 of file probdist.cpp.

                                                                       {
     if (data.empty()) {
         return 0.0; // Invalid input, return 0
     }
  
     std::vector<double> sortedData = data;
     std::sort(sortedData.begin(), sortedData.end());
  
     size_t size = sortedData.size();
     if (size % 2 == 0) {
         return (sortedData[size / 2 - 1] + sortedData[size / 2]) / 2.0;
     } else {
         return sortedData[size / 2];
     }
 }

◆ mle()

double gpmp::stats::ProbDist::mle ( const std::vector< double > & data )

Compute the Maximum Likelihood Estimate (MLE) for the mean of a dataset.

Parameters

data	The dataset

Returns: The MLE estimate for the mean

Definition at line 199 of file probdist.cpp.

                                                            {
     if (data.empty()) {
         return 0.0; // Invalid input, return 0
     }
  
     double sum = std::accumulate(data.begin(), data.end(), 0.0);
     return sum / data.size();
 }

◆ mle_est()

double gpmp::stats::ProbDist::mle_est ( const std::vector< double > & data )

Placeholder function for M-estimation.

Parameters

data	The dataset

Returns: The M-estimation result

Definition at line 220 of file probdist.cpp.

                                                                {
     // This is a placeholder, you can replace it with a specific M-estimation
     // method
     return mle(data);
 }

◆ mom()

double gpmp::stats::ProbDist::mom ( const std::vector< double > & data )

Compute the method of moments (MOM) estimate for the mean of a dataset.

Parameters

data	The dataset

Returns: The MOM estimate for the mean

Definition at line 208 of file probdist.cpp.

                                                            {
     if (data.empty()) {
         return 0.0; // Invalid input, return 0
     }
     gpmp::stats::Describe desc;
  
     double mean = desc.mean_arith(data);
     double variance = desc.variance(data, mean);
  
     return mean - variance / 2.0;
 }

References gpmp::stats::Describe::mean_arith(), and gpmp::stats::Describe::variance().

◆ mumv()

double gpmp::stats::ProbDist::mumv ( const std::vector< double > & data )

Compute the Mean-Unbiased Minimum-Variance (MUMV) estimate for the mean of a dataset.

Parameters

data	The dataset

Returns: The MUMV estimate for the mean

Definition at line 226 of file probdist.cpp.

                                                             {
     if (data.empty()) {
         return 0.0; // Invalid input, return 0
     }
  
     double sum = std::accumulate(data.begin(), data.end(), 0.0);
     return sum / data.size();
 }

◆ normal_CDF()

double gpmp::stats::ProbDist::normal_CDF	(	double	x,
		double	mean,
		double	stddev
	)

Compute the cumulative distribution function (CDF) for the normal distribution.

Parameters

x	The value at which to evaluate the CDF
mean	The mean of the distribution
stddev	The standard deviation of the distribution

Returns: The CDF value at the given point

Definition at line 135 of file probdist.cpp.

                                                                          {
     // Implement the cumulative distribution function (CDF) for the normal
     // distribution You can use standard libraries or existing implementations
     // for this calculation Example using C++ standard library:
     return 0.5 * (1.0 + std::erf((x - mean) / (stddev * std::sqrt(2.0))));
 }

◆ normal_PDF()

double gpmp::stats::ProbDist::normal_PDF	(	double	x,
		double	mean,
		double	stddev
	)

Compute the probability density function (PDF) for the normal distribution.

Parameters

x	The value at which to evaluate the PDF
mean	The mean of the distribution
stddev	The standard deviation of the distribution

Returns: The PDF value at the given point

Definition at line 127 of file probdist.cpp.

                                                                          {
     // Implement the probability density function (PDF) for the normal
     // distribution You can use standard libraries or existing implementations
     // for this calculation Example using C++ standard library:
     double exponent = -0.5 * std::pow((x - mean) / stddev, 2.0);
     return (1.0 / (stddev * std::sqrt(2.0 * M_PI))) * std::exp(exponent);
 }

◆ Pivot()

double gpmp::stats::ProbDist::Pivot	(	const std::vector< double > &	data,
		double	pivotFunctionconst std::vector< double > &
	)

Compute the value of a pivot function for interval estimation.

Parameters

data	The dataset
pivotFunction	The pivot function to evaluate

Returns: The value of the pivot function

Definition at line 271 of file probdist.cpp.

                                                      {
     if (data.empty()) {
         return 0.0; // Invalid input, return 0
     }
  
     return pivotFunction(data);
 }

◆ PivotFunctionForConfidenceInterval()

double gpmp::stats::ProbDist::PivotFunctionForConfidenceInterval ( const std::vector< double > & data )

Example pivot function for computing a confidence interval.

Parameters

data	The dataset

Returns: The value of the pivot function for a confidence interval

Definition at line 282 of file probdist.cpp.

                                    {
     size_t n = data.size();
  
     gpmp::stats::Describe desc;
     double mean = desc.mean_arith(data);
     double stddev = desc.stdev(data, mean);
  
     return mean + 2 * stddev / std::sqrt(static_cast<double>(n));
 }

References gpmp::stats::Describe::mean_arith(), and gpmp::stats::Describe::stdev().

◆ PredictionInterval()

std::pair< double, double > gpmp::stats::ProbDist::PredictionInterval	(	const std::vector< double > &	data,
		double	alpha
	)

Compute the prediction interval for a given dataset and significance level.

Parameters

data	The dataset
alpha	The significance level

Returns: A pair representing the lower and upper bounds of the prediction interval

Definition at line 310 of file probdist.cpp.

                                                         {
     if (data.empty() || alpha <= 0.0 || alpha >= 1.0) {
         return {0.0, 0.0}; // Invalid input, return an empty interval
     }
  
     // Placeholder, implement prediction interval calculation
     double lowerBound = 0.0;
     double upperBound = 1.0;
  
     return {lowerBound, upperBound};
 }

◆ quantile_dist()

double gpmp::stats::ProbDist::quantile_dist ( double probability )

Compute the quantile of the standard normal distribution.

Parameters

probability The probability value between 0 and 1

Returns: The quantile corresponding to the given probability

Definition at line 116 of file probdist.cpp.

                                                           {
     if (probability <= 0.0 || probability >= 1.0) {
         return 0.0; // Invalid input, return 0
     }
  
     // Using erfinv for older C++ standards
     double z = std::sqrt(2.0) * erfinv(2.0 * probability - 1.0);
  
     return z;
 }

References erfinv().

◆ ToleranceInterval()

std::pair< double, double > gpmp::stats::ProbDist::ToleranceInterval	(	const std::vector< double > &	data,
		double	alpha
	)

Compute the tolerance interval for a given dataset and significance level.

Parameters

data	The dataset
alpha	The significance level

Returns: A pair representing the lower and upper bounds of the tolerance interval

Definition at line 324 of file probdist.cpp.

                                                        {
     if (data.empty() || alpha <= 0.0 || alpha >= 1.0) {
         return {0.0, 0.0}; // Invalid input, return an empty interval
     }
  
     // Placeholder, implement tolerance interval calculation
     double lowerBound = 0.0;
     double upperBound = 1.0;
  
     return {lowerBound, upperBound};
 }

◆ uniform_CDF()

double gpmp::stats::ProbDist::uniform_CDF	(	size_t	k,
		size_t	n
	)

Compute the cumulative distribution function (CDF) for the uniform distribution.

Parameters

k	The value at which to evaluate the CDF
n	The maximum value in the uniform distribution

Returns: The CDF value at the given point

Definition at line 142 of file probdist.cpp.

                                                         {
     if (k == 0 || k > n) {
         return 0.0; // Invalid input, return 0
     }
  
     return static_cast<double>(k) / (n + 1);
 }

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

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

Public Member Functions

Detailed Description

Member Function Documentation

◆ ConfidenceInterval()

◆ emp_CDF()

◆ emp_PMF()

◆ exp_PDF()

◆ inverse_emp_CDF()

◆ LikelihoodInterval()

◆ median_uniased()

◆ mle()

◆ mle_est()

◆ mom()

◆ mumv()

◆ normal_CDF()

◆ normal_PDF()

◆ Pivot()

◆ PivotFunctionForConfidenceInterval()

◆ PredictionInterval()

◆ quantile_dist()

◆ ToleranceInterval()

◆ uniform_CDF()