Class FoldedNormalDistribution.HalfNormalDistribution

  • All Implemented Interfaces:
    ContinuousDistribution
    Enclosing class:
    FoldedNormalDistribution

    private static class FoldedNormalDistribution.HalfNormalDistribution
    extends FoldedNormalDistribution
    Specialisation for the half-normal distribution.

    Elimination of the mu location parameter simplifies the probability functions and allows computation of the log density and inverse CDF/SF.

    • Field Detail

      • VAR

        private static final double VAR
        Variance constant (1 - 2/pi). Computed using Matlab's VPA to 30 digits.
        See Also:
        Constant Field Values
      • logSigmaPlusHalfLog2Pi

        private final double logSigmaPlusHalfLog2Pi
        The value of log(sigma) + 0.5 * log(2*PI) stored for faster computation.
    • Constructor Detail

      • HalfNormalDistribution

        HalfNormalDistribution​(double sigma)
        Parameters:
        sigma - Scale parameter.
    • Method Detail

      • density

        public double density​(double x)
        Description copied from interface: ContinuousDistribution
        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 - Point at which the PDF is evaluated.
        Returns:
        the value of the probability density function at x.
      • probability

        public double probability​(double x0,
                                  double x1)
        Description copied from class: AbstractContinuousDistribution
        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:
        probability in interface ContinuousDistribution
        Overrides:
        probability in class AbstractContinuousDistribution
        Parameters:
        x0 - Lower bound (exclusive).
        x1 - Upper bound (inclusive).
        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.
      • logDensity

        public double logDensity​(double x)
        Description copied from interface: ContinuousDistribution
        Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
        Parameters:
        x - Point at which the PDF is evaluated.
        Returns:
        the logarithm of the value of the probability density function at x.
      • cumulativeProbability

        public double cumulativeProbability​(double x)
        Description copied from interface: ContinuousDistribution
        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.
        Parameters:
        x - 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.
      • survivalProbability

        public double survivalProbability​(double x)
        Description copied from interface: ContinuousDistribution
        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 complementary cumulative distribution function.

        By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

        Parameters:
        x - Point at which the survival function is evaluated.
        Returns:
        the probability that a random variable with this distribution takes a value greater than x.
      • inverseSurvivalProbability

        public double inverseSurvivalProbability​(double p)
        Computes the inverse survival probability function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

        \[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb R : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]

        By default, this is defined as inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.

        The default implementation returns:

        Specified by:
        inverseSurvivalProbability in interface ContinuousDistribution
        Overrides:
        inverseSurvivalProbability in class AbstractContinuousDistribution
        Parameters:
        p - Survival probability.
        Returns:
        the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).
      • getMean

        public double getMean()
        Description copied from class: FoldedNormalDistribution
        Gets the mean of this distribution.

        For location parameter \( \mu \) and scale parameter \( \sigma \), the mean is:

        \[ \sigma \sqrt{ \frac 2 \pi } \exp \left( \frac{-\mu^2}{2\sigma^2} \right) + \mu \operatorname{erf} \left( \frac \mu {\sqrt{2\sigma^2}} \right) \]

        where \( \operatorname{erf} \) is the error function.

        Specified by:
        getMean in interface ContinuousDistribution
        Specified by:
        getMean in class FoldedNormalDistribution
        Returns:
        the mean.