Statistical methods, classes, and functions. More...

Classes
class	Anova
	one-way ANOVA More...

class	AUC
	Area Under ROC Curve. More...

struct	Average
	Functor to take average of a range. More...

class	Averager
	Class to calculate simple (first and second moments) averages. More...

struct	averager

class	Averager1
	class to calculate mean More...

class	Averager3
	class to calculate 1st, 2nd, and 3rd central moments More...

class	Averager4
	class to calculate 1st, 2nd, 3rd, and 4th central moments More...

class	averager_base
	Base class for averager classes. More...

class	averager_base2
	Base class for averagers calculating mean and variance. More...

class	averager_base3

class	averager_base4

struct	averager_pair

struct	averager_traits

struct	averager_traits< utility::unweighted_iterator_tag >

struct	averager_traits< utility::weighted_iterator_tag >

class	AveragerPair
	Class for taking care of mean and covariance of two variables. More...

class	AveragerPairWeighted
	Class for taking care of mean and covariance of two variables in a weighted manner. More...

class	AveragerWeighted
	Class to calulate averages with weights. More...

class	Chi2
	Chi squared test. More...

class	Distance
	A convenience class to implement Distance. More...

class	EuclideanDistance
	Calculates the Euclidean distance between elements of two ranges. More...

class	Fisher
	Fisher's exact test. More...

class	FoldChange
	Score given by the difference by the group means. More...

class	GaussianMixture
	Data modelled as mixture of Gaussian distributions. More...

class	Histogram
	Histograms provide a convenient way of presenting the distribution of a set of data. More...

class	Kendall
	Kendall's tau rank coefficient. More...

class	KolmogorovSmirnov
	Kolmogorov Smirnov Test. More...

class	KolmogorovSmirnovOneSample
	Kolmogorov Smirnov Test for one class. More...

class	LikelihoodRatioTestBinomial
	Likelihood-ratio test for binomial data. More...

struct	Max
	Larget element. More...

struct	Mean
	Mean element. More...

struct	Median
	Median element. More...

struct	Min
	Smallest element. More...

class	NegativeBinomialExtendedMixture

class	NegativeBinomialMixture

class	Nth_Element

class	Pearson
	Class for calculating Pearson correlation. More...

class	PearsonCorrelation
	Class for calculating Pearson correlation. More...

struct	PearsonDistance
	Calculates the Pearson correlation distance between two points given by elements of ranges. More...

class	PercentileConfidenceInterval

class	Percentiler
	Functor to calculate percentile of a range. More...

class	PoissonMixture
	Infer Poissonian mixed model. More...

class	ROC
	Reciever Operating Characteristic. More...

class	SAMScore
	Class for score used in Significance Analysis of Microarrays (SAM). More...

class	Score
	Interface Class for score classes. More...

class	Smoother
	Estimating a distribution in a smooth fashion. More...

class	SNRScore
	Class for score based on signal-to-noise ratio (SNRScore). More...

class	Spearman
	Spearman rank correlation coefficient. More...

class	tScore
	Class for Fisher's t-test. More...

class	tTest
	Class for Student's t-test. More...

class	TukeyBiweightEstimator
	Tukey's Biweight Estimator. More...

struct	VectorFunction
	Interface Class for vector functors. More...

class	WilcoxonFoldChange
	WilcoxonFoldChange. More...

Functions
template<typename T , typename ForwardIterator >
void	add (T &o, ForwardIterator first, ForwardIterator last, const classifier::Target &target)

template<typename BidirectionalIterator1 , typename BidirectionalIterator2 >
void	benjamini_hochberg (BidirectionalIterator1 first, BidirectionalIterator1 last, BidirectionalIterator2 result)
	Benjamini Hochberg multiple test correction. More...

template<typename RandomAccessIterator , typename MutableRandomAccessIterator >
void	benjamini_hochberg_unsorted (RandomAccessIterator first, RandomAccessIterator last, MutableRandomAccessIterator result)
	Benjamini Hochberg multiple test correction. More...

double	cdf_hypergeometric_P (unsigned int k, unsigned int n1, unsigned int n2, unsigned int t)

utility::Matrix	correlation (const utility::MatrixBase &x)

template<typename InputIterator >
double	entropy (InputIterator first, InputIterator last)

double	pearson_p_value (double r, unsigned int n)
	one-sided p-value More...

double	kurtosis (const utility::VectorBase &)
	Computes the kurtosis of the data in a vector. More...

template<class RandomAccessIterator >
double	mad (RandomAccessIterator first, RandomAccessIterator last, bool sorted=false)
	Median absolute deviation from median. More...

template<class RandomAccessIterator >
double	median (RandomAccessIterator first, RandomAccessIterator last, bool sorted=false)

template<class T >
double	mutual_information (const T &A)
	Calculates the mutual information of A. More...

template<class RandomAccessIterator >
double	percentile (RandomAccessIterator first, RandomAccessIterator last, double p, bool sorted=false)

template<class RandomAccessIterator >
double	percentile2 (RandomAccessIterator first, RandomAccessIterator last, double p, bool sorted=false)

double	skewness (const utility::VectorBase &)
	Computes the skewness of the data in a vector. More...

Detailed Description

Statistical methods, classes, and functions.

All classes and functions related to statistical methods or functions are defined within this namespace. See Weighted Statistics.

Function Documentation

◆ add()

template<typename T , typename ForwardIterator >

void theplu::yat::statistics::add	(	T &	o,
		ForwardIterator	first,
		ForwardIterator	last,
		const classifier::Target &	target
	)

Adding a range [first, last) into an object of type T. The requirements for the type T is to have an add(double, bool, double) function.

Type Requirements:

ForwardIterator is a Readable Iterator
ForwardIterator is Single Pass Iterator

◆ benjamini_hochberg()

template<typename BidirectionalIterator1 , typename BidirectionalIterator2 >

void theplu::yat::statistics::benjamini_hochberg	(	BidirectionalIterator1	first,
		BidirectionalIterator1	last,
		BidirectionalIterator2	result
	)

Benjamini Hochberg multiple test correction.

Given a sorted range of p-values such that $p_1 \le p_2 \le ... \le p_N$ a Benjamnini-Hochberg corrected p-value, q, is calculated recursively as $ q_i = $ min $(p_i \frac{N}{i}, q_{i+1})$ with the anchor constraint that $ q_m = p_m $ .

Type Requirements:

BidirectionalIterator1 is a Readable Iterator
BidirectionalIterator1 is a Bidirectional Traversal Iterator
BidirectionalIterator1::value type is convertible to double
BidirectionalIterator2 is a Readable Iterator
BidirectionalIterator2 is a Writable Iterator
BidirectionalIterator2 is a Bidirectional Traversal Iterator
double is convertible to BidirectionalIterator2::value_type

Since: New in yat 0.8

◆ benjamini_hochberg_unsorted()

template<typename RandomAccessIterator , typename MutableRandomAccessIterator >

void theplu::yat::statistics::benjamini_hochberg_unsorted	(	RandomAccessIterator	first,
		RandomAccessIterator	last,
		MutableRandomAccessIterator	result
	)

Benjamini Hochberg multiple test correction.

Similar to benjamini_hochberg() but does not assume that input range, [first, last), is sorted. The resulting range is the same as if sorting input range, call benjamini_hochberg, and unsort the result range.

Type Requirements:

RandomAccessIterator is a Readable Iterator
RandomAccessIterator is a Random Access Traversal Iterator
RandomAccessIterator::value type is convertible to double
MutableRandomAccessIterator is a Readable Iterator
MutableRandomAccessIterator is a Writable Iterator
MutableRandomAccessIterator is a Random Access Traversal Iterator
double is convertible to MutableRandomAccessIterator::value_type

Since: New in yat 0.13

◆ cdf_hypergeometric_P()

double theplu::yat::statistics::cdf_hypergeometric_P	(	unsigned int	k,
		unsigned int	n1,
		unsigned int	n2,
		unsigned int	t
	)

Calculates the probability to get k or smaller from a hypergeometric distribution with parameters n1 n2 t. Hypergeomtric situation you get in the following situation: Let there be n1 ways for a "good" selection and n2 ways for a "bad" selection out of a total of possibilities. Take t samples without replacement and k of those are "good" samples. k will follow a hypergeomtric distribution.

Returns: cumulative hypergeomtric distribution functions P(k).

◆ correlation()

utility::Matrix theplu::yat::statistics::correlation ( const utility::MatrixBase & x )

Calculates the Pearson correlation between each pair of columns.

Returns: a symmetric matrix with correlations

Since: New in yat 0.16

◆ entropy()

template<typename InputIterator >

double theplu::yat::statistics::entropy	(	InputIterator	first,
		InputIterator	last
	)

The entropy is calculated as $- \sum_i p_i \log p_i$ where $p_i = \frac{n_i}{\sum_j n_j}$

Requirements:

InputIterator must be a Readable Iterator
InputIterator must be a Single Pass Iterator
InputIterator::value_type must be convertible to double

Since: New in yat 0.12

◆ kurtosis()

double theplu::yat::statistics::kurtosis ( const utility::VectorBase & )

Computes the kurtosis of the data in a vector.

The kurtosis measures how sharply peaked a distribution is, relative to its width. The kurtosis is normalized to zero for a gaussian distribution.

◆ mad()

template<class RandomAccessIterator >

double theplu::yat::statistics::mad	(	RandomAccessIterator	first,
		RandomAccessIterator	last,
		bool	sorted = `false`
	)

Median absolute deviation from median.

Function is non-mutable function

Type Requirements:

RandomAccessIterator must be a Data Iterator
RandomAccessIterator must be a Random Access Traversal Iterator
For unweighted iterator, RandomAccessIterator must be an Lvalue Iterator as implied by Forward Iterator.

Since 0.6 function also work with a Weighted Iterator

◆ median()

template<class RandomAccessIterator >

double theplu::yat::statistics::median	(	RandomAccessIterator	first,
		RandomAccessIterator	last,
		bool	sorted = `false`
	)

Median is defined to be value in the middle. If number of values is even median is the average of the two middle values. the median value is given by p equal to 50. If sorted is false (default), the range is copied, the copy is sorted, and then used to calculate the median.

Function is a non-mutable function, i.e., first and last can be const_iterators.

Type Requirements:

RandomAccessIterator must be a Data Iterator
RandomAccessIterator must be a Random Access Traversal Iterator
For unweighted iterator, RandomAccessIterator must be an Lvalue Iterator as implied by Forward Iterator.

Returns: median of range

◆ mutual_information()

template<class T >

double theplu::yat::statistics::mutual_information ( const T & A )

Calculates the mutual information of A.

The elements in A are unnormalized probabilies of the joint distribution.

The mutual information is calculated as $\sum \sum p(x,y) \log_2 \frac {p(x,y)} {p(x)p(y)}$ where $p(x,y) = \frac {A_{xy}}{\sum_{x,y} A_{xy}}$ ; $p(x) = \sum_y A_{xy} / \sum_{x,y} A_{xy}$ ; $p(y) = \sum_x A_{xy} / \sum_{x,y} A_{xy}$

Requirements:

T must be a model of Container2D
T::value_type must be convertible to double

Returns: mutual information in bits; if you want in natural base multiply with M_LN2 (defined in gsl/gsl_math.h )

Since: New in yat 0.12

◆ pearson_p_value()

double theplu::yat::statistics::pearson_p_value	(	double	r,
		unsigned int	n
	)

one-sided p-value

This function uses the t-distribution to calculate the one-sided p-value. Given that the true correlation is zero (Null hypothesis) the estimated correlation, r, after a transformation is t-distributed:

$\sqrt{(n-2)} \frac{r}{\sqrt{(1-r^2)}} \in t(n-2)$

Returns: Probability that correlation is larger than r by chance when having n samples. For r larger or equal to 1.0, 0.0 is returned. For r smaller or equal to -1.0, 1.0 is returned.

◆ percentile()

template<class RandomAccessIterator >

double theplu::yat::statistics::percentile	(	RandomAccessIterator	first,
		RandomAccessIterator	last,
		double	p,
		bool	sorted = `false`
	)

The percentile is determined by the p, a number between 0 and

The percentile is found by interpolation, using the formula $percentile = (1 - \delta) x_i + \delta x_{i+1}$ where p is floor and $\delta$ is .Thus the minimum value of the vector is given by p equal to zero, the maximum is given by p equal to 100 and the median value is given by p equal to 50. If sorted is false (default), the vector is copied, the copy is sorted, and then used to calculate the median.

Function is a non-mutable function, i.e., first and last can be const_iterators.

Requirements: RandomAccessIterator is an iterator over a range of doubles (or any type being convertable to double).

Returns: p'th percentile of range

Deprecated:: percentile2 will replace this function in the future

Note: the definition of percentile used here is not identical to that one used in percentile2 and Percentile. The difference is smaller for large ranges.

◆ percentile2()

template<class RandomAccessIterator >

double theplu::yat::statistics::percentile2	(	RandomAccessIterator	first,
		RandomAccessIterator	last,
		double	p,
		bool	sorted = `false`
	)

See also: Percentiler

Type Requirements:

RandomAccessIterator must be a Data Iterator
RandomAccessIterator must be a Random Access Traversal Iterator
For unweighted iterator, RandomAccessIterator must be an Lvalue Iterator as implied by Forward Iterator.

Since: new in yat 0.5

◆ skewness()

double theplu::yat::statistics::skewness ( const utility::VectorBase & )

Computes the skewness of the data in a vector.

The skewness measures the asymmetry of the tails of a distribution.

Classes

Functions

Detailed Description

Function Documentation

◆ add()

◆ benjamini_hochberg()

◆ benjamini_hochberg_unsorted()

◆ cdf_hypergeometric_P()

◆ correlation()

◆ entropy()

◆ kurtosis()

◆ mad()

◆ median()

◆ mutual_information()

◆ pearson_p_value()

◆ percentile()

◆ percentile2()

◆ skewness()