distributions

Type Members

1. abstract class AbstractContinuousDistr[T] extends GenericDistribution[T] with ContinuousDistr[T]

   

2. abstract class AbstractDiscreteDistr[T] extends GenericDistribution[T] with DiscreteDistr[T]

   

3. case class BlockedMESN(tau: Double, alpha: PartitionedVector, mu: PartitionedVector, sigma: PartitionedPSDMatrix) extends SkewSymmDistribution[PartitionedVector] with Moments[PartitionedVector, PartitionedPSDMatrix] with Product with Serializable

   

   Extended Multivariate Skew-Gaussian distribution as specified in Adcock and Schutes, defined on PartitionedVector

   Extended Multivariate Skew-Gaussian distribution as specified in Adcock and Schutes, defined on PartitionedVector

   tau

   Determines the cutoff of the warping function

   alpha

   A breeze DenseVector which represents the skewness parameters

   mu

   The center of the distribution

   sigma

   The covariance matrix of the base multivariate gaussian.

4. case class BlockedMultiVariateGaussian(mean: PartitionedVector, covariance: PartitionedPSDMatrix)(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[PartitionedVector] with Moments[PartitionedVector, PartitionedPSDMatrix] with HasErrorBars[PartitionedVector] with Product with Serializable

   

   Represents a Gaussian distribution over a PartitionedVector

5. case class BlockedMultivariateStudentsT(mu: Double, mean: PartitionedVector, covariance: PartitionedPSDMatrix)(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[PartitionedVector] with Moments[PartitionedVector, PartitionedPSDMatrix] with HasErrorBars[PartitionedVector] with Product with Serializable

   

6. case class Erlang(shape: Int, rate: Double)(implicit rand: RandBasis = Rand) extends ContinuousDistr[Double] with HasCdf with Moments[Double, Double] with Product with Serializable

   

   The Erlang distribution was developed by A.

   Erlang Distribution.

   The Erlang distribution was developed by A. K. Erlang to examine the number of telephone calls which might be made at the same time to the operators of the switching stations. This work on telephone traffic engineering has been expanded to consider waiting times in queueing systems in general. The distribution is now used in the fields of stochastic processes and of biomathematics.

7. case class ExtendedMultivariateSkewNormal(tau: Double, alpha: DenseVector[Double], mu: DenseVector[Double], sigma: DenseMatrix[Double]) extends SkewSymmDistribution[DenseVector[Double]] with Product with Serializable

   

   Extended Multivariate Skew-Gaussian distribution as specified in Azzalani et.al.

   Extended Multivariate Skew-Gaussian distribution as specified in Azzalani et.al.

   tau

   Determines the cutoff of the warping function

   alpha

   A breeze DenseVector which represents the skewness parameters

   mu

   The center of the distribution

   sigma

   The covariance matrix of the base multivariate gaussian.

8. case class ExtendedSkewGaussian(alpha0: Double, alpha: Double, mu: Double = 0.0, sigma: Double = 1.0)(implicit rand: RandBasis = Rand) extends SkewSymmDistribution[Double] with Product with Serializable

   

   The univariate extended skew gaussian distribution

9. abstract class GenericDistribution[T] extends Density[T] with Rand[T] with Serializable

   

10. trait HasErrorBars[T] extends Serializable

    

    Distributions which can generate confidence intervals around their mean can extend this trait and override the confidenceInterval method .

11. case class Kumaraswamy(a: Double, b: Double)(implicit rand: RandBasis = Rand) extends ContinuousDistr[Double] with HasCdf with Moments[Double, Double] with Product with Serializable

    

    A probability distribution for a univariate random variable which takes values in the interval [0, 1].

    Kumaraswamy Distribution

    A probability distribution for a univariate random variable which takes values in the interval [0, 1]. The Kumaraswamy distribution is closely related to the Beta distribution.

12. case class MESN(tau: Double, alpha: DenseVector[Double], mu: DenseVector[Double], sigma: DenseMatrix[Double]) extends SkewSymmDistribution[DenseVector[Double]] with Product with Serializable

    

    Extended Multivariate Skew-Gaussian distribution as specified in Adcock and Schutes.

    Extended Multivariate Skew-Gaussian distribution as specified in Adcock and Schutes.

    tau

    Determines the cutoff of the warping function

    alpha

    A breeze DenseVector which represents the skewness parameters

    mu

    The center of the distribution

    sigma

    The covariance matrix of the base multivariate gaussian.

13. class MVGaussian extends AbstractContinuousDistr[DenseVector[Double]] with Moments[DenseVector[Double], DenseMatrix[Double]] with HasErrorBars[DenseVector[Double]]

    

14. case class MatrixNormal(m: DenseMatrix[Double], u: DenseMatrix[Double], v: DenseMatrix[Double])(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[DenseMatrix[Double]] with Moments[DenseMatrix[Double], (DenseMatrix[Double], DenseMatrix[Double])] with HasErrorBars[DenseMatrix[Double]] with Product with Serializable

    

    Matrix normal distribution over n × p matrices

    Matrix normal distribution over n × p matrices

    m

    The mode, mean and center of the distribution

    u

    The n × n covariance matrix of the rows

    v

    The p × p covariance matrix of the columns

15. case class MatrixT(mu: Double, m: DenseMatrix[Double], omega: DenseMatrix[Double], sigma: DenseMatrix[Double])(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[DenseMatrix[Double]] with Moments[DenseMatrix[Double], (DenseMatrix[Double], DenseMatrix[Double])] with HasErrorBars[DenseMatrix[Double]] with Product with Serializable

    

    Matrix Students T distribution over n × p matrices

    Matrix Students T distribution over n × p matrices

    mu

    Degrees of freedom

    m

    The mode, mean and center of the distribution

    omega

    The p × p covariance matrix of the columns

    sigma

    The n × n covariance matrix of the rows

    Annotations

    @Experimental()

16. class MixtureDistribution[I] extends AbstractContinuousDistr[I]

    

    Distribution consisting of a mixture of components and a probability weight over each component.

17. class MixtureWithConfBars[I, V] extends MixtureDistribution[I] with HasErrorBars[I]

    

    A mixture distribution which can compute its mean and generate confidence intervals.

    A mixture distribution which can compute its mean and generate confidence intervals.

    I

    The domain of the random variable

    V

    The type of the variance returned by the mixture components

18. case class MultivariateSkewNormal(alpha: DenseVector[Double], mu: DenseVector[Double], sigma: DenseMatrix[Double]) extends SkewSymmDistribution[DenseVector[Double]] with Product with Serializable

    

    Multivariate Skew-Normal distribution as specified in Azzalani et.

    Multivariate Skew-Normal distribution as specified in Azzalani et. al.

    alpha

    A breeze DenseVector which represents the skewness parameters

    mu

    The center of the distribution

    sigma

    The covariance matrix of the base multivariate gaussian.

19. case class MultivariateStudentsT(mu: Double, mean: DenseVector[Double], covariance: DenseMatrix[Double])(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[DenseVector[Double]] with Moments[DenseVector[Double], DenseMatrix[Double]] with HasErrorBars[DenseVector[Double]] with Product with Serializable

    

    Represents a multivariate students t distribution

    Represents a multivariate students t distribution

    mu

    The degrees of freedom

    mean

    The mean vector

    covariance

    Covariance matrix

20. case class MultivariateUniform(low: DenseVector[Double], high: DenseVector[Double])(implicit rand: RandBasis = Rand) extends ContinuousDistr[DenseVector[Double]] with Moments[DenseVector[Double], DenseVector[Double]] with Product with Serializable

    

    Created by mandar on 25/09/2016.

21. case class SkewGaussian(alpha: Double, mu: Double = 0.0, sigma: Double = 1.0) extends SkewSymmDistribution[Double] with Product with Serializable

    

    Univariate skew gaussian distribution

22. abstract class SkewSymmDistribution[T] extends ContinuousDistr[T]

    

    A generalised skew symmetric distribution has the following components

    A generalised skew symmetric distribution has the following components

    • φ: A symmetric distribution acting as the base
    • G: A symmetric distribution acting as the warping function
    • w: An odd function from the domain type T to Double.
    • τ: Cutoff

    The probability density of a generalised skew symmetric distribution is

    ρ(x) = φ(x)*G(w(x) + τ)

23. case class TruncatedGaussian(mu: Double, sigma: Double, a: Double, b: Double)(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[Double] with HasCdf with HasInverseCdf with Moments[Double, Double] with Product with Serializable

    

    Univariate Truncated Gaussian Distribution

    Univariate Truncated Gaussian Distribution

    mu

    The mean of the base gaussian.

    sigma

    Std Deviation of the base gaussian.

    a

    Lower limit of truncation.

    b

    Upper limit of truncation.

24. case class UESN(tau: Double, alpha: Double, mu: Double = 0.0, sigma: Double = 1.0)(implicit rand: RandBasis = Rand) extends SkewSymmDistribution[Double] with Product with Serializable

    

    The univariate version of MESN of Adcock and Schutes.

    The univariate version of MESN of Adcock and Schutes.

    See also: MESN

25. class UnivariateGaussian extends Gaussian with HasErrorBars[Double]

    

26. case class UnivariateStudentsT(mu: Double, mean: Double, sigma: Double)(implicit rand: RandBasis = Rand) extends AbstractContinuousDistr[Double] with Moments[Double, Double] with HasErrorBars[Double] with Product with Serializable