org.apache.commons.math3.distribution
Class NormalDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractRealDistribution
      org.apache.commons.math3.distribution.NormalDistribution

All Implemented Interfaces:

Serializable, RealDistribution

public class NormalDistribution
extends AbstractRealDistribution

Implementation of the normal (gaussian) distribution.

Version:

$Id: NormalDistribution.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Normal distribution (Wikipedia), Normal distribution (MathWorld), Serialized Form

Field Summary

static double

DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

NormalDistribution()
Create a normal distribution with mean equal to zero and standard deviation equal to one.

NormalDistribution(double mean, double sd)
Create a normal distribution using the given mean and standard deviation.

NormalDistribution(double mean, double sd, double inverseCumAccuracy)
Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.

NormalDistribution(RandomGenerator rng, double mean, double sd, double inverseCumAccuracy)
Creates a normal distribution.

Method Summary

double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	cumulativeProbability(double x0, double x1) Deprecated. See RealDistribution.cumulativeProbability(double,double)
double	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getMean() Access the mean.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
protected double	getSolverAbsoluteAccuracy() Returns the solver absolute accuracy for inverse cumulative computation.
double	getStandardDeviation() Access the standard deviation.
double	getSupportLowerBound() Access the lower bound of the support.
double	getSupportUpperBound() Access the upper bound of the support.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
boolean	isSupportLowerBoundInclusive() Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive() Whether or not the upper bound of support is in the domain of the density function.
double	probability(double x0, double x1) For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
double	sample() Generate a random value sampled from this distribution.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

inverseCumulativeProbability, probability, reseedRandomGenerator, sample

Methods inherited from class java.lang.Object

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

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

NormalDistribution

public NormalDistribution()

Create a normal distribution with mean equal to zero and standard deviation equal to one.

NormalDistribution

public NormalDistribution(double mean,
                          double sd)
                   throws NotStrictlyPositiveException

Create a normal distribution using the given mean and standard deviation.

Parameters:

mean - Mean for this distribution.

sd - Standard deviation for this distribution.

Throws:

NotStrictlyPositiveException - if sd <= 0.

NormalDistribution

public NormalDistribution(double mean,
                          double sd,
                          double inverseCumAccuracy)
                   throws NotStrictlyPositiveException

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.

Throws:

NotStrictlyPositiveException - if sd <= 0.

Since:

2.1

NormalDistribution

public NormalDistribution(RandomGenerator rng,
                          double mean,
                          double sd,
                          double inverseCumAccuracy)
                   throws NotStrictlyPositiveException

Creates a normal distribution.

Parameters:

rng - Random number generator.

mean - Mean for this distribution.

sd - Standard deviation for this distribution.

inverseCumAccuracy - Inverse cumulative probability accuracy.

Throws:

NotStrictlyPositiveException - if sd <= 0.

Since:

3.1

Method Detail

getMean

public double getMean()

Access the mean.

Returns:

the mean for this distribution.

getStandardDeviation

public double getStandardDeviation()

Access the standard deviation.

Returns:

the standard deviation for this distribution.

density

public double density(double x)

Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

cumulativeProbability

public double cumulativeProbability(double x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. If x is 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.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

cumulativeProbability

@Deprecated
public double cumulativeProbability(double x0,
                                               double x1)
                             throws NumberIsTooLargeException

Deprecated. See RealDistribution.cumulativeProbability(double,double)

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity

P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

Specified by:

cumulativeProbability in interface RealDistribution

Overrides:

cumulativeProbability in class AbstractRealDistribution

Parameters:

x0 - the exclusive lower bound

x1 - the inclusive upper bound

Returns:

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint

Throws:

NumberIsTooLargeException - if x0 > x1

probability

public double probability(double x0,
                          double x1)
                   throws NumberIsTooLargeException

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Overrides:

probability in class AbstractRealDistribution

Parameters:

x0 - Lower bound (excluded).

x1 - Upper bound (included).

Returns:

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

Throws:

NumberIsTooLargeException - if x0 > x1. The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:

getSolverAbsoluteAccuracy in class AbstractRealDistribution

Returns:

the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For mean parameter mu, the mean is mu.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For standard deviation parameter s, the variance is s^2.

Returns:

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

public double getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always negative infinity no matter the parameters.

Returns:

lower bound of the support (always Double.NEGATIVE_INFINITY)

getSupportUpperBound

public double getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:

true

sample

public double sample()

Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Specified by:

sample in interface RealDistribution

Overrides:

sample in class AbstractRealDistribution

Returns:

a random value.