dev.nm.stat.test.distribution.normality

Class ShapiroWilkDistribution

java.lang.Object

dev.nm.stat.test.distribution.normality.ShapiroWilkDistribution

All Implemented Interfaces:

ProbabilityDistribution

public class ShapiroWilkDistribution
extends Object
implements ProbabilityDistribution

Shapiro-Wilk distribution is the distribution of the Shapiro-Wilk statistics, which tests the null hypothesis that a sample comes from a normally distributed population.

This is an implementation of ALGORITHM AS R94. Although our implementation allows for sample size > 5000, its validity is not rigorously established.

See Also:

• Patrick Royston, "A Remark on Algorithm AS 181: The W Test for Normality," Applied Statistics, 44, 547-551, 1995.
• Patrick Royston, "Approximating the Shapiro-Wilk W-test for non-normality," Statistics and Computing, Volume 2, Number 3, 117-119.
• Patrick Royston, "Algorithm AS 181: The W Test for Normality," Applied Statistics, 31, 176-180, 1982.
• Wikipedia: Shapiro-Wilk test

Constructor Summary

Constructors

Constructor and Description
ShapiroWilkDistribution(int n) Construct a Shapiro-Wilk distribution.

Method Summary

Modifier and Type	Method and Description
double	cdf(double W) Gets the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x) Deprecated.
double	entropy() Deprecated.
double	kurtosis() Deprecated.
double	mean() Deprecated.
double	median() Deprecated.
double	moment(double x) Deprecated.
double	quantile(double u) Deprecated.
double	skew() Deprecated.
double	variance() Deprecated.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ShapiroWilkDistribution

public ShapiroWilkDistribution(int n)

Construct a Shapiro-Wilk distribution.

Parameters:

n - the number of observations

Method Detail

mean

@Deprecated
public double mean()

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the mean of this distribution.

Specified by:

mean in interface ProbabilityDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

@Deprecated
public double median()

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the median of this distribution.

Specified by:

median in interface ProbabilityDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

@Deprecated
public double variance()

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the variance of this distribution.

Specified by:

variance in interface ProbabilityDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

@Deprecated
public double skew()

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the skewness of this distribution.

Specified by:

skew in interface ProbabilityDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

@Deprecated
public double kurtosis()

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the excess kurtosis of this distribution.

Specified by:

kurtosis in interface ProbabilityDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

@Deprecated
public double entropy()

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the entropy of this distribution.

Specified by:

entropy in interface ProbabilityDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double W)

Description copied from interface: ProbabilityDistribution

Gets the cumulative probability F(x) = Pr(X ≤ x).

Specified by:

cdf in interface ProbabilityDistribution

Parameters:

W - x

Returns:

F(x) = Pr(X ≤ x)

See Also:

Wikipedia: Cumulative distribution function

quantile

@Deprecated
public double quantile(double u)

Deprecated.

Description copied from interface: ProbabilityDistribution

Gets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time. \[ \begin{gathered} F^{-1}(u) = x, such that \\ Pr(X \le x) = u \end{gathered} \] This may not always exist.

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

u - u, a quantile

Returns:

\(F^{-1}(u)\)

See Also:

Wikipedia: Quantile function

density

@Deprecated
public double density(double x)

Deprecated.

Description copied from interface: ProbabilityDistribution

The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space. \[ f(x) = dF(X) / dx \] This may not always exist.

For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.

Specified by:

density in interface ProbabilityDistribution

Parameters:

x - x

Returns:

f(x)

See Also:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

moment

@Deprecated
public double moment(double x)

Deprecated.

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of \(e^{tX}\). That is, \[ E(e^{tX}) \] This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

x - t

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function