C# Класс Accord.Statistics.Distributions.Univariate.KolmogorovSmirnovDistribution

Наследование: UnivariateContinuousDistribution, IFormattable
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Открытые методы

Метод Описание
Clone ( ) : object

Creates a new object that is a copy of the current instance.
ComplementaryDistributionFunction ( double x ) : double

Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.

The Complementary Cumulative Distribution Function (CCDF) is the complement of the Cumulative Distribution Function, or 1 minus the CDF.

ComplementaryDistributionFunction ( double n, double x ) : double

Computes the Complementary Cumulative Distribution Function (1-CDF) for the Kolmogorov-Smirnov statistic's distribution.
CumulativeFunction ( double n, double x ) : double

Computes the Cumulative Distribution Function (CDF) for the Kolmogorov-Smirnov statistic's distribution.

This function computes the cumulative probability P[Dn <= x] of the Kolmogorov-Smirnov distribution using multiple methods as suggested by Richard Simard (2010).

Simard partitioned the problem of evaluating the CDF using multiple approximation and asymptotic methods in order to achieve a best compromise between speed and precision. This function follows the same partitioning as Simard, which is described in the table below.

For n <= 140 and: 1/n > x >= 1-1/nUses the Ruben-Gambino formula. 1/n < nx² < 0.754693Uses the Durbin matrix algorithm. 0.754693 <= nx² < 4Uses the Pomeranz algorithm. 4 <= nx² < 18Uses the complementary distribution function. nx² >= 18Returns the constant 1. For 140 < n <= 10^5 nx² >= 18Returns the constant 1. nx^(3/2) < 1.4Durbin matrix algorithm. nx^(3/2) > 1.4Pelz-Good asymptotic series. For n > 10^5 nx² >= 18Returns the constant 1. nx² < 18Pelz-Good asymptotic series.
DistributionFunction ( double x ) : double

Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.

The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.

Durbin ( int n, double d ) : double

Durbin's algorithm for computing P[Dn < d]

The method presented by Marsaglia (2003), as stated in the paper, is based on a succession of developments starting with Kolmogorov and culminating in a masterful treatment by Durbin (1972). Durbin's monograph summarized and extended many previous works published in the years 1933-73.

This function implements the small C procedure provided by Marsaglia on his paper with corrections made by Simard (2010). Further optimizations also have been performed.

References: - Marsaglia, G., Tsang, W. W., Wang, J. (2003) "Evaluating Kolmogorov's Distribution", Journal of Statistical Software, 8 (18), 1–4. jstor. Available on: http://www.jstatsoft.org/v08/i18/paper - Durbin, J. (1972) Distribution Theory for Tests Based on The Sample Distribution Function, Society for Industrial & Applied Mathematics, Philadelphia.
Fit ( double observations, double weights, Fitting options ) : void

Not supported.
KolmogorovSmirnovDistribution ( [ samples ) : System

Creates a new Kolmogorov-Smirnov distribution.
LogProbabilityDensityFunction ( double x ) : double

Not supported.
OneSideDistributionFunction ( double x ) : double

Computes the Upper Tail of the P[Dn >= x] distribution.

This function approximates the upper tail of the P[Dn >= x] distribution using the one-sided Kolmogorov-Smirnov statistic.

OneSideUpperTail ( double n, double x ) : double

Computes the Upper Tail of the P[Dn >= x] distribution.

This function approximates the upper tail of the P[Dn >= x] distribution using the one-sided Kolmogorov-Smirnov statistic.

PelzGood ( double n, double x ) : double

Pelz-Good algorithm for computing lower-tail areas of the Kolmogorov-Smirnov distribution.

As stated in Simard's paper, Pelz and Good (1976) generalized Kolmogorov's approximation to an asymptotic series in 1/sqrt(n).

References: Wolfgang Pelz and I. J. Good, "Approximating the Lower Tail-Areas of the Kolmogorov-Smirnov One-Sample Statistic", Journal of the Royal Statistical Society, Series B. Vol. 38, No. 2 (1976), pp. 152-156
Pomeranz ( int n, double x ) : double

Pomeranz algorithm.
ProbabilityDensityFunction ( double x ) : double

Not supported.
ToString ( string format, IFormatProvider formatProvider ) : string

Returns a System.String that represents this instance.

Приватные методы

Метод Описание
computeA ( int n, double A, double z ) : void

Creates matrix A of the Pomeranz algorithm.
computeH ( int n, double A, double H ) : double

Computes matrix H of the Pomeranz algorithm.
computeLimits ( double t, double floors, double ceilings ) : double

Initializes the Pomeranz algorithm.
matrixPower ( double A, int eA, double V, int &eV, int m, int n, double B ) : void

Computes matrix power. Used in the Durbin algorithm.

Описание методов

Clone() публичный Метод

Creates a new object that is a copy of the current instance.
public Clone ( ) : object
Результат object

ComplementaryDistributionFunction() публичный Метод

Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
The Complementary Cumulative Distribution Function (CCDF) is the complement of the Cumulative Distribution Function, or 1 minus the CDF.
public ComplementaryDistributionFunction ( double x ) : double
x double
Результат double

ComplementaryDistributionFunction() публичный статический Метод

Computes the Complementary Cumulative Distribution Function (1-CDF) for the Kolmogorov-Smirnov statistic's distribution.
public static ComplementaryDistributionFunction ( double n, double x ) : double
n double The sample size.
x double The Kolmogorov-Smirnov statistic.
Результат double

CumulativeFunction() публичный статический Метод

Computes the Cumulative Distribution Function (CDF) for the Kolmogorov-Smirnov statistic's distribution.

This function computes the cumulative probability P[Dn <= x] of the Kolmogorov-Smirnov distribution using multiple methods as suggested by Richard Simard (2010).

Simard partitioned the problem of evaluating the CDF using multiple approximation and asymptotic methods in order to achieve a best compromise between speed and precision. This function follows the same partitioning as Simard, which is described in the table below.

For n <= 140 and: 1/n > x >= 1-1/nUses the Ruben-Gambino formula. 1/n < nx² < 0.754693Uses the Durbin matrix algorithm. 0.754693 <= nx² < 4Uses the Pomeranz algorithm. 4 <= nx² < 18Uses the complementary distribution function. nx² >= 18Returns the constant 1. For 140 < n <= 10^5 nx² >= 18Returns the constant 1. nx^(3/2) < 1.4Durbin matrix algorithm. nx^(3/2) > 1.4Pelz-Good asymptotic series. For n > 10^5 nx² >= 18Returns the constant 1. nx² < 18Pelz-Good asymptotic series.
public static CumulativeFunction ( double n, double x ) : double
n double The sample size.
x double The Kolmogorov-Smirnov statistic.
Результат double

DistributionFunction() публичный Метод

Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
public DistributionFunction ( double x ) : double
x double A single point in the distribution range.
Результат double

Durbin() публичный статический Метод

Durbin's algorithm for computing P[Dn < d]

The method presented by Marsaglia (2003), as stated in the paper, is based on a succession of developments starting with Kolmogorov and culminating in a masterful treatment by Durbin (1972). Durbin's monograph summarized and extended many previous works published in the years 1933-73.

This function implements the small C procedure provided by Marsaglia on his paper with corrections made by Simard (2010). Further optimizations also have been performed.

References: - Marsaglia, G., Tsang, W. W., Wang, J. (2003) "Evaluating Kolmogorov's Distribution", Journal of Statistical Software, 8 (18), 1–4. jstor. Available on: http://www.jstatsoft.org/v08/i18/paper - Durbin, J. (1972) Distribution Theory for Tests Based on The Sample Distribution Function, Society for Industrial & Applied Mathematics, Philadelphia.
public static Durbin ( int n, double d ) : double
n int
d double
Результат double

Fit() публичный Метод

Not supported.
public Fit ( double observations, double weights, Fitting options ) : void
observations double
weights double
options Fitting
Результат void

KolmogorovSmirnovDistribution() публичный Метод

Creates a new Kolmogorov-Smirnov distribution.
public KolmogorovSmirnovDistribution ( [ samples ) : System
samples [ The number of samples.
Результат System

LogProbabilityDensityFunction() публичный Метод

Not supported.
public LogProbabilityDensityFunction ( double x ) : double
x double
Результат double

OneSideDistributionFunction() публичный Метод

Computes the Upper Tail of the P[Dn >= x] distribution.
This function approximates the upper tail of the P[Dn >= x] distribution using the one-sided Kolmogorov-Smirnov statistic.
public OneSideDistributionFunction ( double x ) : double
x double
Результат double

OneSideUpperTail() публичный статический Метод

Computes the Upper Tail of the P[Dn >= x] distribution.
This function approximates the upper tail of the P[Dn >= x] distribution using the one-sided Kolmogorov-Smirnov statistic.
public static OneSideUpperTail ( double n, double x ) : double
n double
x double
Результат double

PelzGood() публичный статический Метод

Pelz-Good algorithm for computing lower-tail areas of the Kolmogorov-Smirnov distribution.

As stated in Simard's paper, Pelz and Good (1976) generalized Kolmogorov's approximation to an asymptotic series in 1/sqrt(n).

References: Wolfgang Pelz and I. J. Good, "Approximating the Lower Tail-Areas of the Kolmogorov-Smirnov One-Sample Statistic", Journal of the Royal Statistical Society, Series B. Vol. 38, No. 2 (1976), pp. 152-156

public static PelzGood ( double n, double x ) : double
n double
x double
Результат double

Pomeranz() публичный статический Метод

Pomeranz algorithm.
public static Pomeranz ( int n, double x ) : double
n int
x double
Результат double

ProbabilityDensityFunction() публичный Метод

Not supported.
public ProbabilityDensityFunction ( double x ) : double
x double
Результат double

ToString() публичный Метод

Returns a System.String that represents this instance.
public ToString ( string format, IFormatProvider formatProvider ) : string
format string
formatProvider IFormatProvider
Результат string