org.apache.commons.math4.distribution

## Class NormalDistribution

• ### Nested classes/interfaces inherited from interface org.apache.commons.math4.distribution.RealDistribution

RealDistribution.Sampler
• ### Field Summary

Fields
Modifier and Type Field and Description
static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
• ### Fields inherited from class org.apache.commons.math4.distribution.AbstractRealDistribution

SOLVER_DEFAULT_ABSOLUTE_ACCURACY
• ### Constructor Summary

Constructors
Constructor and Description
NormalDistribution()
Create a normal distribution with mean equal to zero and standard deviation equal to one.
NormalDistribution(double mean, double sd)
Creates a distribution.
NormalDistribution(double mean, double sd, double inverseCumAccuracy)
Creates a distribution.
• ### Method Summary

All Methods
Modifier and Type Method and Description
RealDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
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.
double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e.
double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
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).
• ### Methods inherited from class org.apache.commons.math4.distribution.AbstractRealDistribution

probability, 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
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
Creates a distribution.
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
Creates a distribution.
Parameters:
mean - Mean for this distribution.
sd - Standard deviation for this distribution.
inverseCumAccuracy - Inverse cumulative probability accuracy.
Throws:
NotStrictlyPositiveException - if sd <= 0.
• ### 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
• #### logDensity

public double logDensity(double x)
Returns the natural logarithm of 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. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double).

The default implementation simply computes the logarithm of density(x).

Specified by:
logDensity in interface RealDistribution
Overrides:
logDensity in class AbstractRealDistribution
Parameters:
x - the point at which the PDF is evaluated
Returns:
the logarithm of 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
• #### inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
throws OutOfRangeException
Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
• inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in R | P(X<=x) > 0} for p = 0.
The default implementation returns
Specified by:
inverseCumulativeProbability in interface RealDistribution
Overrides:
inverseCumulativeProbability in class AbstractRealDistribution
Parameters:
p - the cumulative probability
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
Throws:
OutOfRangeException - if p < 0 or p > 1
Since:
3.2
• #### 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).
Specified by:
probability in interface RealDistribution
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)
• #### 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
• #### createSampler

public RealDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
Specified by:
createSampler in interface RealDistribution
Overrides:
createSampler in class AbstractRealDistribution
Parameters:
rng - Generator of uniformly distributed numbers.
Returns:
a sampler that produces random numbers according this distribution.