Class FoldedNormalDistribution.RegularFoldedNormalDistribution

java.lang.Object
org.apache.commons.statistics.distribution.AbstractContinuousDistribution
org.apache.commons.statistics.distribution.FoldedNormalDistribution
org.apache.commons.statistics.distribution.FoldedNormalDistribution.RegularFoldedNormalDistribution
All Implemented Interfaces:
ContinuousDistribution
Enclosing class:
FoldedNormalDistribution
private static class FoldedNormalDistribution.RegularFoldedNormalDistribution extends FoldedNormalDistribution
Regular implementation of the folded normal distribution.
Since:
1.1

  • Field Details

    • mu

      private final double mu
      The location.

    • mean

      private final double mean
      Cached value for inverse probability function.

    • variance

      private final double variance
      Cached value for inverse probability function.

  • Constructor Details

    • RegularFoldedNormalDistribution

      RegularFoldedNormalDistribution(double mu, double sigma)
      Parameters:
      mu - Location parameter.
      sigma - Scale parameter.

  • Method Details

    • getMu

      public double getMu()
      Description copied from class: FoldedNormalDistribution
      Gets the location parameter \( \mu \) of this distribution.
      Specified by:
      getMu in class FoldedNormalDistribution
      Returns:
      the mu parameter.

    • 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.

    • 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.

    • 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.

    • getVariance

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

      For location parameter \( \mu \), scale parameter \( \sigma \) and a distribution mean \( \mu_Y \), the variance is:

      \[ \mu^2 + \sigma^2 - \mu_{Y}^2 \]

      Specified by:
      getVariance in interface ContinuousDistribution
      Specified by:
      getVariance in class FoldedNormalDistribution
      Returns:
      the variance.

    • createSampler

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