Kolmogorov Smirnov Test. More...

#include <yat/statistics/KolmogorovSmirnov.h>

Classes
struct	Element

Public Member Functions
	KolmogorovSmirnov (void)
	Constructor.

void	add (double value, bool class_label, double weight=1.0)
	add a value

template<typename ForwardIterator >
void	add (ForwardIterator first, ForwardIterator last)
	add a range More...

double	p_value (void) const
	Large-Sample Approximation. More...

double	p_value (size_t perm) const
	p-value More...

void	remove (double value, bool class_label, double weight=1.0)
	Remove a data point. More...

void	reset (void)
	resets everything to zero

double	score (void) const
	Kolmogorov Smirnov statistic. More...

void	scores (std::vector< double > &) const

void	shuffle (void)
	shuffle class labels More...

double	signed_score (void) const

Related Functions
(Note that these are not member functions.)
std::ostream &	operator<< (std::ostream &, const KolmogorovSmirnov &)
	output operator

Detailed Description

Kolmogorov Smirnov Test.

Member Function Documentation

◆ add()

template<typename ForwardIterator >

void theplu::yat::statistics::KolmogorovSmirnov::add	(	ForwardIterator	first,
		ForwardIterator	last
	)

add a range

Type Requirements:

ForwardIterator models Readable Iterator
ForwardIterator models Forward Traversal Iterator
value_type of ForwardIterator must be convertible to KolmogorovSmirnov::Element

Insertion takes typically N*log(N). However, if range is sorted, insertion takes linear time. A common use case of this function is when calculating several KS statistics on a data set (values and weights) with different class labels.

Since: New in yat 0.5

◆ p_value() [1/2]

double theplu::yat::statistics::KolmogorovSmirnov::p_value ( void ) const

Large-Sample Approximation.

This analytical approximation of p-value can be used when all weight equal unity and sample sizes n and m are large. The p-value is calcuated as $P = \displaystyle - 2 \sum_{k=1}^{\infty} (-1)^ke^{-2k^2s^2}$ , where s is the scaled score:

$s = \sqrt\frac{nm}{n+m}$ score().

Since: New in yat 0.5

Following Hollander and Wolfe

◆ p_value() [2/2]

double theplu::yat::statistics::KolmogorovSmirnov::p_value ( size_t perm ) const

p-value

Performs a permutation test using perm label randomizations and calculate how often a score equal or larger than score() is obtained.

See also: shuffle

◆ remove()

void theplu::yat::statistics::KolmogorovSmirnov::remove	(	double	value,
		bool	class_label,
		double	weight = `1.0`
	)

Remove a data point.

Exceptions

utility::runtime_error if no data point exist with value, class_label, and weight.

Since: New in yat 0.9

◆ score()

double theplu::yat::statistics::KolmogorovSmirnov::score ( void ) const

Kolmogorov Smirnov statistic.

Returns: absolute value of signed_score()

$sup_x | F_{\textrm{True}}(x) - F_{\textrm{False}}(x) |$ where $F(x) = \frac{\sum_{i:x_i\le x}w_i}{ \sum w_i}$

See also: scores()

◆ scores()

void theplu::yat::statistics::KolmogorovSmirnov::scores ( std::vector< double > & ) const

In case of no ties and data points are sorted such that $x_i \le x_{i+1}$ , the kth element is calculated as

$s[k] = \frac{\sum_i^k I(y_i=1) w_i}{ \sum I(y_i=1) w_i} - \frac{\sum_i^k I(y_i=0) w_i}{ \sum I(y_i=0) w_i}$ .

In case $ x_k $ has tied values the sums include all values tied with $ x_k $ , i.e., $i : x_i \le x_k$ .

Since: Part of public interface since yat 0.21

◆ shuffle()

void theplu::yat::statistics::KolmogorovSmirnov::shuffle ( void )

shuffle class labels

This is equivalent to reset and re-add values with shuffled class labels.

Since: New in yat 0.5

◆ signed_score()

double theplu::yat::statistics::KolmogorovSmirnov::signed_score ( void ) const

Same as score() but keeping the sign, in other words, abs(signed_score())==score()

Of the values calculated in scores(), return the one with the greatest deviation from zero.

A positive score implies that values in class true on average are smaller than values in class false.

Since: New in yat 0.5

See also: scores()

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

yat/statistics/KolmogorovSmirnov.h

Classes

Public Member Functions

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