Constructor Detail

Method Detail

• mvph_joint

   final static Double mvph_joint(DoubleArray alpha, Matrix S, Matrix T, Matrix D, Integer n1, Integer n2)

  Computes the joint moment EX^n1 * Y^n2 of a bivariate phase-type distribution.

  The bivariate phase-type distribution has:

  • Initial vector alpha

  • First phase transition matrix S (for X)

  • Transition matrix D between phases (from X completion to Y start)

  • Second phase transition matrix T (for Y)

  Formula: EX^n1 * Y^n2 = n1! * n2! * alpha * inv(-S)^(n1+1) * D * inv(-T)^(n2+1) * (-T) * e

  Parameters:

  alpha - Initial probability vector

  S - First phase generator matrix (for X)

  T - Second phase generator matrix (for Y)

  D - Transition matrix between phases

  n1 - Power for first variable X

  n2 - Power for second variable Y

  Returns:

  Joint moment EX^n1 * Y^n2

• mvph_mean_x

   final static Double mvph_mean_x(DoubleArray alpha, Matrix S, Matrix T, Matrix D)

  Computes the mean of the first variable in a bivariate PH distribution. EX = mvph_joint(alpha, S, T, D, 1, 0)

• mvph_mean_y

   final static Double mvph_mean_y(DoubleArray alpha, Matrix S, Matrix T, Matrix D)

  Computes the mean of the second variable in a bivariate PH distribution. EY = mvph_joint(alpha, S, T, D, 0, 1)

• mvph_cov

   final static Double mvph_cov(DoubleArray alpha, Matrix S, Matrix T, Matrix D)

  Computes the covariance of a bivariate PH distribution. Cov(X, Y) = EXY - EX*EY

• mvph_corr

   final static Double mvph_corr(DoubleArray alpha, Matrix S, Matrix T, Matrix D)

  Computes the correlation of a bivariate PH distribution. Corr(X, Y) = Cov(X, Y) / (StdDev(X) * StdDev(Y))