butools.dph.MomentsFromMG¶

butools.dph.MomentsFromMG()¶

Matlab:	moms = MomentsFromMG(alpha, A, K, prec)
Mathematica:	moms = MomentsFromMG[alpha, A, K, prec]
Python/Numpy:	moms = MomentsFromMG(alpha, A, K, prec)

Returns the first K moments of a matrix geometric distribution.

Parameters:

alpha : vector, shape (1,M) The initial vector of the matrix-geometric distribution. The sum of the entries of alpha is less or equal to 1. A : matrix, shape (M,M) The matrix parameter of the matrix-geometric distribution. K : int, optional Number of moments to compute. If K=0, 2*M-1 moments are computed. The default value is 0. prec : double, optional Numerical precision for checking the input. The default value is 1e-14.

Returns:

moms : row vector of doubles The vector of moments.

Examples

For Matlab:

>>> a = [-0.6,0.3,1.3];
>>> A = [0.25, 0.2, -0.15; 0.3, 0.1, 0.25; 0, 0.2, 0.47];
>>> moms = MomentsFromMG(a, A);
>>> disp(moms);
       3.4675       16.203       97.729       731.45       6576.8
>>> moms = MomentsFromMG(a, A, 3);
>>> disp(moms);
       3.4675       16.203       97.729

For Mathematica:

>>> a = {-0.6,0.3,1.3};
>>> A = {{0.25, 0.2, -0.15},{0.3, 0.1, 0.25},{0, 0.2, 0.47}};
>>> moms = MomentsFromMG[a, A];
>>> Print[moms];
{3.467473524962178, 16.2025761585682, 97.7286502495287, 731.4453438525275, 6576.785916679157}
>>> moms = MomentsFromMG[a, A, 3];
>>> Print[moms];
{3.467473524962178, 16.2025761585682, 97.7286502495287}

For Python/Numpy:

>>> a = ml.matrix([[-0.6,0.3,1.3]])
>>> A = ml.matrix([[0.25, 0.2, -0.15],[0.3, 0.1, 0.25],[0, 0.2, 0.47]])
>>> moms = MomentsFromMG(a, A)
>>> print(moms)
[3.4674735249621778, 16.202576158568199, 97.728650249528698, 731.44534385252746, 6576.7859166791568]
>>> moms = MomentsFromMG(a, A, 3)
>>> print(moms)
[3.4674735249621778, 16.202576158568199, 97.728650249528698]