Package org.apache.commons.math3.distribution

Class NormalDistribution

    • 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

      • serialVersionUID

        private static final long serialVersionUID
        Serializable version identifier.
        See Also:
        Constant Field Values

      • SQRT2

        private static final double SQRT2
        √(2)

      • mean

        private final double mean
        Mean of this distribution.

      • standardDeviation

        private final double standardDeviation
        Standard deviation of this distribution.

      • logStandardDeviationPlusHalfLog2Pi

        private final double logStandardDeviationPlusHalfLog2Pi
        The value of log(sd) + 0.5*log(2*pi) stored for faster computation.

      • solverAbsoluteAccuracy

        private final double solverAbsoluteAccuracy
        Inverse cumulative probability accuracy.

    • Constructor Detail

      • NormalDistribution

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

        Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

      • NormalDistribution

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

        Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

        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.

        Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

        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

      • 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).
        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

      • 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