Package jline.api.moment

Class Moment_joint_binomial_from_tail

java.lang.Object
jline.api.moment.Moment_joint_binomial_from_tail
public final class Moment_joint_binomial_from_tail extends Object
Joint binomial moments from joint survival probabilities.

For a nonnegative integer random vector with joint survival array t_(m_1,...,m_d) = P(N_1 >= m_1, ..., N_d >= m_d), 

   b_(k) = E[prod_j nchoosek(N_j,k_j)]
         = sum_(m>=k) prod_j nchoosek(m_j-1,k_j-1) * t_(m)

The transform is the tensor product of the univariate one, which is what makes the mode-by-mode evaluation legitimate: an entry with k_j = 0 selects m_j = 0, and t_(0,m_2,...) is by construction the marginal survival array of the remaining coordinates. As in the univariate case it is upper triangular, so the array must cover the joint support to be exact.

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003.

Since:
LINE 3.0

  • Method Details

    • moment_joint_binomial_from_tail

      public static double[] moment_joint_binomial_from_tail(double[] t, int[] dims)
      Converts joint survival probabilities into joint binomial moments.
      Parameters:
      t - flattened joint survival array in row-major order
      dims - extents of the array, dims[j] = n_j+1
      Returns:
      flattened joint binomial moments, same layout