de.lmu.ifi.dbs.elki.math.statistics.distribution

Class NormalDistribution

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

de.lmu.ifi.dbs.elki.math.statistics.distribution.NormalDistribution

All Implemented Interfaces:

Distribution, Parameterizable

@Alias(value={"GaussianDistribution","normal","gauss"})
public class NormalDistribution
extends AbstractDistribution

Gaussian distribution aka normal distribution

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	NormalDistribution.Parameterizer Parameterization class

Field Summary

Fields

Modifier and Type	Field and Description
(package private) static double[]	ERFAPP_A Coefficients for erf approximation.
(package private) static double[]	ERFAPP_B Coefficients for erf approximation.
(package private) static double[]	ERFAPP_C Coefficients for erf approximation.
(package private) static double[]	ERFAPP_D Coefficients for erf approximation.
(package private) static double[]	ERFAPP_P Coefficients for erf approximation.
(package private) static double[]	ERFAPP_Q Coefficients for erf approximation.
(package private) static double[]	ERFINV_A Coefficients for erfinv approximation, rational version
(package private) static double[]	ERFINV_B Coefficients for erfinv approximation, rational version
(package private) static double[]	ERFINV_C Coefficients for erfinv approximation, rational version
(package private) static double[]	ERFINV_D Coefficients for erfinv approximation, rational version
private double	mean Mean value for the generator
static double	ONEBYPHIINV075 1 / CDFINV(0.75)
(package private) static double	P_HIGH Treshold for switching nethods for erfinv approximation
(package private) static double	P_LOW Treshold for switching nethods for erfinv approximation
private double	stddev Standard deviation

Fields inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

random

Constructor Summary

Constructors

Constructor and Description
NormalDistribution(double mean, double stddev) Constructor for Gaussian distribution
NormalDistribution(double mean, double stddev, Random random) Constructor for Gaussian distribution
NormalDistribution(double mean, double stddev, RandomFactory random) Constructor for Gaussian distribution

Method Summary

Methods

Modifier and Type	Method and Description
double	cdf(double val) Return the cumulative density function at the given value.
static double	cdf(double x, double mu, double sigma) Cumulative probability density function (CDF) of a normal distribution.
static double	erf(double x) Error function for Gaussian distributions = Normal distributions.
static double	erfc(double x) Complementary error function for Gaussian distributions = Normal distributions.
static double	erfinv(double x) Inverse error function.
double	getMean()
double	getStddev()
double	nextRandom() Generate a new random value
double	pdf(double val) Return the density of an existing value
static double	pdf(double x, double mu, double sigma) Probability density function of the normal distribution.
double	quantile(double q) Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double x, double mu, double sigma) Inverse cumulative probability density function (probit) of a normal distribution.
static double	standardNormalCDF(double x) Cumulative probability density function (CDF) of a normal distribution.
static double	standardNormalPDF(double x) Probability density function of the normal distribution.
static double	standardNormalQuantile(double d) Approximate the inverse error function for normal distributions.
String	toString() Describe the distribution

Methods inherited from class java.lang.Object

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

Field Detail

ERFAPP_A

static final double[] ERFAPP_A

Coefficients for erf approximation. Loosely based on http://www.netlib.org/specfun/erf

ERFAPP_B

static final double[] ERFAPP_B

Coefficients for erf approximation. Loosely based on http://www.netlib.org/specfun/erf

ERFAPP_C

static final double[] ERFAPP_C

Coefficients for erf approximation. Loosely based on http://www.netlib.org/specfun/erf

ERFAPP_D

static final double[] ERFAPP_D

Coefficients for erf approximation. Loosely based on http://www.netlib.org/specfun/erf

ERFAPP_P

static final double[] ERFAPP_P

Coefficients for erf approximation. Loosely based on http://www.netlib.org/specfun/erf

ERFAPP_Q

static final double[] ERFAPP_Q

Coefficients for erf approximation. Loosely based on http://www.netlib.org/specfun/erf

P_LOW

static final double P_LOW

Treshold for switching nethods for erfinv approximation

See Also:

Constant Field Values

P_HIGH

static final double P_HIGH

Treshold for switching nethods for erfinv approximation

See Also:

Constant Field Values

ERFINV_A

static final double[] ERFINV_A

Coefficients for erfinv approximation, rational version

ERFINV_B

static final double[] ERFINV_B

Coefficients for erfinv approximation, rational version

ERFINV_C

static final double[] ERFINV_C

Coefficients for erfinv approximation, rational version

ERFINV_D

static final double[] ERFINV_D

Coefficients for erfinv approximation, rational version

ONEBYPHIINV075

public static final double ONEBYPHIINV075

1 / CDFINV(0.75)

See Also:

Constant Field Values

mean

private double mean

Mean value for the generator

stddev

private double stddev

Standard deviation

Constructor Detail

NormalDistribution

public NormalDistribution(double mean,
                  double stddev,
                  RandomFactory random)

Constructor for Gaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

random - Random generator

NormalDistribution

public NormalDistribution(double mean,
                  double stddev,
                  Random random)

Constructor for Gaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

random - Random generator

NormalDistribution

public NormalDistribution(double mean,
                  double stddev)

Constructor for Gaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

Method Detail

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Parameters:

val - existing value

Returns:

distribution density

cdf

public double cdf(double val)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Parameters:

val - existing value

Returns:

cumulative density

quantile

public double quantile(double q)

Description copied from interface: Distribution

Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.

Parameters:

q - Quantile to find

Returns:

Quantile position

nextRandom

public double nextRandom()

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Overrides:

nextRandom in class AbstractDistribution

Returns:

new random value

toString

public String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class Object

Returns:

description

getMean

public double getMean()

Returns:

the mean

getStddev

public double getStddev()

Returns:

the standard deviation

erfc

public static double erfc(double x)

Complementary error function for Gaussian distributions = Normal distributions. Numerical approximation using taylor series. Implementation loosely based on http://www.netlib.org/specfun/erf

Parameters:

x - parameter value

Returns:

erfc(x)

erf

public static double erf(double x)

Error function for Gaussian distributions = Normal distributions. Numerical approximation using taylor series. Implementation loosely based on http://www.netlib.org/specfun/erf

Parameters:

x - parameter value

Returns:

erf(x)

erfinv

public static double erfinv(double x)

Inverse error function.

Parameters:

x - parameter value

Returns:

erfinv(x)

pdf

public static double pdf(double x,
         double mu,
         double sigma)

Probability density function of the normal distribution.

 1/(SQRT(2*pi*sigma^2)) * e^(-(x-mu)^2/2sigma^2)
 

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

Returns:

PDF of the given normal distribution at x.

standardNormalPDF

public static double standardNormalPDF(double x)

Probability density function of the normal distribution.

 1/(SQRT(2*pi*sigma^2)) * e^(-(x-mu)^2/2sigma^2)
 

Parameters:

x - The value.

Returns:

PDF of the given normal distribution at x.

cdf

public static double cdf(double x,
         double mu,
         double sigma)

Cumulative probability density function (CDF) of a normal distribution.

Parameters:

x - value to evaluate CDF at

mu - Mean value

sigma - Standard deviation.

Returns:

The CDF of the given normal distribution at x.

standardNormalCDF

public static double standardNormalCDF(double x)

Cumulative probability density function (CDF) of a normal distribution.

Parameters:

x - value to evaluate CDF at

Returns:

The CDF of the given normal distribution at x.

quantile

public static double quantile(double x,
              double mu,
              double sigma)

Inverse cumulative probability density function (probit) of a normal distribution.

Parameters:

x - value to evaluate probit function at

mu - Mean value

sigma - Standard deviation.

Returns:

The probit of the given normal distribution at x.

standardNormalQuantile

public static double standardNormalQuantile(double d)

Approximate the inverse error function for normal distributions. Largely based on:

http://www.math.uio.no/~jacklam/notes/invnorm/index.html
by Peter John Acklam

FIXME: precision of this seems to be rather low, compared to our other functions. Only about 8-9 digits agree with SciPy/GNU R.

Parameters:

d - Quantile. Must be in [0:1], obviously.

Returns:

Inverse erf.