Package jdistlib

Class Wishart

java.lang.Object
jdistlib.Wishart
public final class Wishart extends Object
Wishart distribution on symmetric positive-definite matrices.

  • Method Details

    • density

      public static double density(double[][] x, double degreesOfFreedom, double[][] scale, boolean giveLog)
      Density of W_dimension(scale, degreesOfFreedom). The mean under this parameterization is degreesOfFreedom * scale.

    • densityFromCholesky

      public static double densityFromCholesky(double[][] x, double degreesOfFreedom, double[][] lowerCholesky, boolean giveLog)
      Density overload accepting the lower Cholesky factor L of scale.

    • random

      public static double[][] random(double degreesOfFreedom, double[][] lowerCholesky, RandomEngine random)
      Generates one Wishart matrix using Bartlett's decomposition. lowerCholesky is a lower-triangular L with scale = L L'.

    • random

      public static double[][][] random(int count, double degreesOfFreedom, double[][] lowerCholesky, RandomEngine random)
      Generates count matrices while retaining one caller-owned RNG.

    • randomFromScale

      public static double[][] randomFromScale(double degreesOfFreedom, double[][] scale, RandomEngine random)
      Convenience generator accepting the scale matrix rather than its factor.

    • randomFromScale

      public static double[][][] randomFromScale(int count, double degreesOfFreedom, double[][] scale, RandomEngine random)

    • quadraticFormCumulative

      public static double quadraticFormCumulative(double upper, double[] direction, double degreesOfFreedom, double[][] scale, boolean lowerTail, boolean logProbability)
      CDF of the directional variance event direction' W direction <= upper. For W ~ Wishart(df, scale), the quadratic form divided by direction' scale direction is exactly chi-square with df degrees of freedom.

    • standardizedTraceCumulative

      public static double standardizedTraceCumulative(double upper, double degreesOfFreedom, double[][] scale, boolean lowerTail, boolean logProbability)
      CDF of trace(scale^-1 W). This standardized trace is exactly chi-square with dimension * degreesOfFreedom degrees of freedom.

    • determinantProbability

      public static MultivariateProbabilityResult determinantProbability(double lower, double upper, double degreesOfFreedom, double[][] scale, MultivariateProbabilityOptions options, RandomEngine random)
      Computes P(lower <= determinant(W) <= upper). The numerical path conditions on Bartlett's independent chi-square determinant factors and reports randomized-integration error metadata.

    • determinantProbability

      public static MultivariateProbabilityResult determinantProbability(double lower, double upper, double degreesOfFreedom, double[][] scale)

    • determinantCumulative

      public static MultivariateProbabilityResult determinantCumulative(double upper, double degreesOfFreedom, double[][] scale, MultivariateProbabilityOptions options, RandomEngine random)
      Computes P(determinant(W) <= upper).

    • determinantCumulative

      public static MultivariateProbabilityResult determinantCumulative(double upper, double degreesOfFreedom, double[][] scale)

    • logDeterminantProbability

      public static MultivariateProbabilityResult logDeterminantProbability(double lower, double upper, double degreesOfFreedom, double[][] scale, MultivariateProbabilityOptions options, RandomEngine random)
      Computes P(lower <= log(det(W)) <= upper) without exponentiating the caller's thresholds, so extreme determinant events remain representable.

    • logDeterminantProbability

      public static MultivariateProbabilityResult logDeterminantProbability(double lower, double upper, double degreesOfFreedom, double[][] scale)

    • logDeterminantCumulative

      public static MultivariateProbabilityResult logDeterminantCumulative(double upper, double degreesOfFreedom, double[][] scale, MultivariateProbabilityOptions options, RandomEngine random)
      Computes P(log(det(W)) <= upper).

    • logDeterminantCumulative

      public static MultivariateProbabilityResult logDeterminantCumulative(double upper, double degreesOfFreedom, double[][] scale)