java.lang.Object
- org.apache.commons.math.distribution.AbstractDistribution
- - org.apache.commons.math.distribution.AbstractContinuousDistribution
  - - org.apache.commons.math.distribution.NormalDistributionImpl

All Implemented Interfaces:

java.io.Serializable, ContinuousDistribution, Distribution, HasDensity<java.lang.Double>, NormalDistribution
```
public class NormalDistributionImpl
extends AbstractContinuousDistribution
implements NormalDistribution, java.io.Serializable
```
Default implementation of NormalDistribution.

Version:

$Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field Description

static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy
- Fields inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution
  randomData

Constructor Summary

Constructors
Constructor	Description
`NormalDistributionImpl()`	Creates normal distribution with the mean equal to zero and standard deviation equal to one.
`NormalDistributionImpl(double mean, double sd)`	Create a normal distribution using the given mean and standard deviation.
`NormalDistributionImpl(double mean, double sd, double inverseCumAccuracy)`	Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method	Description
`double`	`cumulativeProbability(double x)`	For this distribution, X, this method returns P(X < `x`).
`double`	`density(double x)`	Returns the probability density for a particular point.
`double`	`density(java.lang.Double x)`	Deprecated.
`protected double`	`getDomainLowerBound(double p)`	Access the domain value lower bound, based on `p`, used to bracket a CDF root.
`protected double`	`getDomainUpperBound(double p)`	Access the domain value upper bound, based on `p`, used to bracket a CDF root.
`protected double`	`getInitialDomain(double p)`	Access the initial domain value, based on `p`, used to bracket a CDF root.
`double`	`getMean()`	Access the mean.
`double`	`getNumericalVariance()`	Returns the variance.
`protected double`	`getSolverAbsoluteAccuracy()`	Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
`double`	`getStandardDeviation()`	Access the standard deviation.
`double`	`getSupportLowerBound()`	Returns the lower bound of the support for the distribution.
`double`	`getSupportUpperBound()`	Returns the upper bound of the support for the distribution.
`double`	`inverseCumulativeProbability(double p)`	For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.
`double`	`sample()`	Generates a random value sampled from this distribution.
`void`	`setMean(double mean)`	Deprecated. as of 2.1 (class will become immutable in 3.0)
`void`	`setStandardDeviation(double sd)`	Deprecated. as of 2.1 (class will become immutable in 3.0)

Methods inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution
reseedRandomGenerator, sample

Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution
cumulativeProbability

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.math.distribution.Distribution
cumulativeProbability

- Field Detail
  - DEFAULT_INVERSE_ABSOLUTE_ACCURACY
```
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
```
    Default inverse cumulative probability accuracy
    
    Since:
    
    2.1
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - NormalDistributionImpl
```
public NormalDistributionImpl(double mean,
                              double sd)
```
    Create a normal distribution using the given mean and standard deviation.
    
    Parameters:
    
    mean - mean for this distribution
    
    sd - standard deviation for this distribution
  - NormalDistributionImpl
```
public NormalDistributionImpl(double mean,
                              double sd,
                              double inverseCumAccuracy)
```
    Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.
    
    Parameters:
    
    mean - mean for this distribution
    
    sd - standard deviation for this distribution
    
    inverseCumAccuracy - inverse cumulative probability accuracy
    
    Since:
    
    2.1
  - NormalDistributionImpl
```
public NormalDistributionImpl()
```
    Creates normal distribution with the mean equal to zero and standard deviation equal to one.
- Method Detail
  - getMean
```
public double getMean()
```
    Access the mean.
    
    Specified by:
    
    getMean in interface NormalDistribution
    
    Returns:
    
    mean for this distribution
  - setMean
```
@Deprecated
public void setMean(double mean)
```
    Deprecated.
    as of 2.1 (class will become immutable in 3.0)
    
    Modify the mean.
    
    Specified by:
    
    setMean in interface NormalDistribution
    
    Parameters:
    
    mean - for this distribution
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Access the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface NormalDistribution
    
    Returns:
    
    standard deviation for this distribution
  - setStandardDeviation
```
@Deprecated
public void setStandardDeviation(double sd)
```
    Deprecated.
    as of 2.1 (class will become immutable in 3.0)
    
    Modify the standard deviation.
    
    Specified by:
    
    setStandardDeviation in interface NormalDistribution
    
    Parameters:
    
    sd - standard deviation for this distribution
    
    Throws:
    
    java.lang.IllegalArgumentException - if sd is not positive.
  - density
```
@Deprecated
public double density(java.lang.Double x)
```
    Deprecated.
    
    Return the probability density for a particular point.
    
    Specified by:
    
    density in interface HasDensity<java.lang.Double>
    
    Specified by:
    
    density in interface NormalDistribution
    
    Parameters:
    
    x - The point at which the density should be computed.
    
    Returns:
    
    The pdf at point x.
  - density
```
public double density(double x)
```
    Returns the probability density for a particular point.
    
    Overrides:
    
    density in class AbstractContinuousDistribution
    
    Parameters:
    
    x - The point at which the density should be computed.
    
    Returns:
    
    The pdf at point x.
    
    Since:
    
    2.1
  - cumulativeProbability
```
public double cumulativeProbability(double x)
                             throws MathException
```
    For this distribution, X, this method returns P(X < x). If xis more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is within Double.MIN_VALUE of 0 or 1.
    
    Specified by:
    
    cumulativeProbability in interface Distribution
    
    Parameters:
    
    x - the value at which the CDF is evaluated.
    
    Returns:
    
    CDF evaluated at x.
    
    Throws:
    
    MathException - if the algorithm fails to converge
  - getSolverAbsoluteAccuracy
```
protected double getSolverAbsoluteAccuracy()
```
    Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
    
    Overrides:
    
    getSolverAbsoluteAccuracy in class AbstractContinuousDistribution
    
    Returns:
    
    the solver absolute accuracy
    
    Since:
    
    2.1
  - inverseCumulativeProbability
```
public double inverseCumulativeProbability(double p)
                                    throws MathException
```
    For this distribution, X, this method returns the critical point x, such that P(X < x) = p.
    Returns Double.NEGATIVE_INFINITY for p=0 and Double.POSITIVE_INFINITY for p=1.
    
    Specified by:
    
    inverseCumulativeProbability in interface ContinuousDistribution
    
    Overrides:
    
    inverseCumulativeProbability in class AbstractContinuousDistribution
    
    Parameters:
    
    p - the desired probability
    
    Returns:
    
    x, such that P(X < x) = p
    
    Throws:
    
    MathException - if the inverse cumulative probability can not be computed due to convergence or other numerical errors.
    
    java.lang.IllegalArgumentException - if p is not a valid probability.
  - sample
```
public double sample()
              throws MathException
```
    Generates a random value sampled from this distribution.
    
    Overrides:
    
    sample in class AbstractContinuousDistribution
    
    Returns:
    
    random value
    
    Throws:
    
    MathException - if an error occurs generating the random value
    
    Since:
    
    2.2
  - getDomainLowerBound
```
protected double getDomainLowerBound(double p)
```
    Access the domain value lower bound, based on p, used to bracket a CDF root. This method is used by inverseCumulativeProbability(double) to find critical values.
    
    Specified by:
    
    getDomainLowerBound in class AbstractContinuousDistribution
    
    Parameters:
    
    p - the desired probability for the critical value
    
    Returns:
    
    domain value lower bound, i.e. P(X < lower bound) < p
  - getDomainUpperBound
```
protected double getDomainUpperBound(double p)
```
    Access the domain value upper bound, based on p, used to bracket a CDF root. This method is used by inverseCumulativeProbability(double) to find critical values.
    
    Specified by:
    
    getDomainUpperBound in class AbstractContinuousDistribution
    
    Parameters:
    
    p - the desired probability for the critical value
    
    Returns:
    
    domain value upper bound, i.e. P(X < upper bound) > p
  - getInitialDomain
```
protected double getInitialDomain(double p)
```
    Access the initial domain value, based on p, used to bracket a CDF root. This method is used by inverseCumulativeProbability(double) to find critical values.
    
    Specified by:
    
    getInitialDomain in class AbstractContinuousDistribution
    
    Parameters:
    
    p - the desired probability for the critical value
    
    Returns:
    
    initial domain value
  - getSupportLowerBound
```
public double getSupportLowerBound()
```
    Returns the lower bound of the support for the distribution. The lower bound of the support is always negative infinity no matter the parameters.
    
    Returns:
    
    lower bound of the support (always Double.NEGATIVE_INFINITY)
    
    Since:
    
    2.2
  - getSupportUpperBound
```
public double getSupportUpperBound()
```
    Returns the upper bound of the support for the distribution. The upper bound of the support is always positive infinity no matter the parameters.
    
    Returns:
    
    upper bound of the support (always Double.POSITIVE_INFINITY)
    
    Since:
    
    2.2
  - getNumericalVariance
```
public double getNumericalVariance()
```
    Returns the variance. For standard deviation parameter s, the variance is s^2
    
    Returns:
    
    the variance
    
    Since:
    
    2.2

Class NormalDistributionImpl

Field Summary

Fields inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution

Methods inherited from class java.lang.Object

Methods inherited from interface org.apache.commons.math.distribution.Distribution

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Constructor Detail

NormalDistributionImpl

NormalDistributionImpl

NormalDistributionImpl

Method Detail

getMean

setMean

getStandardDeviation

setStandardDeviation

density

density

cumulativeProbability

getSolverAbsoluteAccuracy

inverseCumulativeProbability

sample

getDomainLowerBound

getDomainUpperBound

getInitialDomain

getSupportLowerBound

getSupportUpperBound

getNumericalVariance