butools.dph.MGFromMoments¶

butools.dph.MGFromMoments()¶

Matlab:	[alpha, A] = MGFromMoments(moms)
Mathematica:	{alpha, A} = MGFromMoments[moms]
Python/Numpy:	alpha, A = MGFromMoments(moms)

Creates a matrix-geometric distribution that has the same moments as given.

Parameters:	moms : vector of doubles The list of moments. The order of the resulting matrix-geometric distribution is determined based on the number of moments given. To obtain a matrix-geometric distribution of order M, 2*M-1 moments are required.
Returns:	alpha : vector, shape (1,M) The initial vector of the matrix-geometric distribution. A : matrix, shape (M,M) The matrix parameter of the matrix-geometric distribution.

References

[R27]

A. van de Liefvoort. The moment problem for continuous distributions. Technical report, University of Missouri, WP-CM-1990-02, Kansas City, 1990.

Examples

For Matlab:

>>> moms = [4.08, 20.41, 130.45, 1054.41, 10463.73];
>>> [a, A] = MGFromMoments(moms);
>>> disp(a);
      0.33333      0.33333      0.33333
>>> disp(A);
      0.15523       1.7289      0.10482
    -0.013774       0.6823    -0.023472
    -0.013847     -0.16787      0.82688
>>> memoms = MomentsFromMG(a, A, 5);
>>> disp(memoms);
         4.08        20.41       130.45       1054.4        10464

For Mathematica:

>>> moms = {4.08, 20.41, 130.45, 1054.41, 10463.73};
>>> {a, A} = MGFromMoments[moms];
>>> Print[a];
{1/3, 1/3, 1/3}
>>> Print[A];
{{0.15522721633282086, 1.7288735256877237, 0.10482133882430097},
 {-0.013773788451490479, 0.6823009288291466, -0.02347241196722473},
 {-0.013846712675345957, -0.1678656131152182, 0.8268849851301606}}
>>> memoms = MomentsFromMG[a, A, 5];
>>> Print[memoms];
{4.080000000000002, 20.41000000000002, 130.4500000000002, 1054.4100000000037, 10463.730000000038}

For Python/Numpy:

>>> moms = [4.08, 20.41, 130.45, 1054.41, 10463.73]
>>> a, A = MGFromMoments(moms)
>>> print(a)
[[ 0.33333  0.33333  0.33333]]
>>> print(A)
[[ 0.15523  1.72887  0.10482]
 [-0.01377  0.6823  -0.02347]
 [-0.01385 -0.16787  0.82688]]
>>> memoms = MomentsFromMG(a, A, 5)
>>> print(memoms)
[4.080000000000001, 20.410000000000029, 130.45000000000047, 1054.4100000000135, 10463.730000000427]