Package sim.util.distribution

Class StudentT

java.lang.Object
sim.util.distribution.AbstractDistribution
sim.util.distribution.AbstractContinuousDistribution
sim.util.distribution.StudentT
All Implemented Interfaces:
Serializable
public class StudentT extends AbstractContinuousDistribution
StudentT distribution (aka T-distribution); See the math definition and animated definition.

p(x) = k * (1+x^2/f) ^ -(f+1)/2 where k = g((f+1)/2) / (sqrt(pi*f) * g(f/2)) and g(a) being the gamma function and f being the degrees of freedom.

Valid parameter ranges: freedom > 0.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation:

Method: Adapted Polar Box-Muller transformation.
This is a port of RandStudentT used in CLHEP 1.4.0 (C++). CLHEP's implementation, in turn, is based on tpol.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

R.W. Bailey (1994): Polar generation of random variates with the t-distribution, Mathematics of Computation 62, 779-781.

See Also:

  • Field Details

    • freedom

      protected double freedom

    • TERM

      protected double TERM

  • Constructor Details

    • StudentT

      public StudentT(double freedom, MersenneTwisterFast randomGenerator)
      Constructs a StudentT distribution. Example: freedom=1.0.
      Parameters:
      freedom - degrees of freedom.
      Throws:
      IllegalArgumentException - if freedom <= 0.0.

  • Method Details

    • cdf

      public double cdf(double x)
      Returns the cumulative distribution function.

    • nextDouble

      public double nextDouble()
      Returns a random number from the distribution.
      Specified by:
      nextDouble in class AbstractDistribution

    • nextDouble

      public double nextDouble(double degreesOfFreedom)
      Returns a random number from the distribution; bypasses the internal state.
      Parameters:
      a - degrees of freedom.
      Throws:
      IllegalArgumentException - if a <= 0.0.

    • pdf

      public double pdf(double x)
      Returns the probability distribution function.

    • setState

      public void setState(double freedom)
      Sets the distribution parameter.
      Parameters:
      freedom - degrees of freedom.
      Throws:
      IllegalArgumentException - if freedom <= 0.0.

    • toString

      public String toString()
      Returns a String representation of the receiver.
      Overrides:
      toString in class Object