NormalDistribution (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

java.lang.Object
- de.lmu.ifi.dbs.elki.math.statistics.distribution.NormalDistribution

All Implemented Interfaces:

Distribution, DistributionWithRandom
```
public class NormalDistribution
extends Object
implements DistributionWithRandom
```
Gaussian distribution aka normal distribution

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
`(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 Random`	`random` The random generator.
`private double`	`stddev` Standard deviation

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

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`	`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
  - mean
```
private double mean
```
    Mean value for the generator
  - stddev
```
private double stddev
```
    Standard deviation
  - random
```
private Random random
```
    The random generator.
- Constructor Detail
  - 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
    
    Specified by:
    
    pdf in interface Distribution
    
    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.
    
    Specified by:
    
    cdf in interface Distribution
    
    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.
    
    Specified by:
    
    quantile in interface Distribution
    
    Parameters:
    q - Quantile to find
    
    Returns:
    Quantile position
  - nextRandom
```
public double nextRandom()
```
    Description copied from interface: DistributionWithRandom
    
    Generate a new random value
    
    Specified by:
    
    nextRandom in interface DistributionWithRandom
    
    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)
  - 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.
  - 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.
  - 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 normal given 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 normal given distribution at x.

Class NormalDistribution

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ERFAPP_A

ERFAPP_B

ERFAPP_C

ERFAPP_D

ERFAPP_P

ERFAPP_Q

P_LOW

P_HIGH

ERFINV_A

ERFINV_B

ERFINV_C

ERFINV_D

mean

stddev

random

Constructor Detail

NormalDistribution

NormalDistribution

Method Detail

pdf

cdf

quantile

nextRandom

toString

getMean

getStddev

erfc

erf

erfinv

standardNormalQuantile

pdf

cdf

quantile