butools.ph.MEFromMoments¶

butools.ph.MEFromMoments()¶

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

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

Parameters:

moms : vector of doubles, length(2*M-1)

The list of moments. The order of the resulting matrix-exponential distribution is determined based on the number of moments given. To obtain a matrix exponential distribution of order M, 2*M-1 moments are required.

Returns:

alpha : matrix, shape (1,M)

The initial vector of the matrix-exponential distribution.

A : matrix, shape (M,M)

The matrix parameter of the matrix-exponential distribution.

References

[R23]

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:

>>> a = [0.1,0.9,0];
>>> A = [-6.2, 2, 0; 2, -9, 1; 1, 0, -3];
>>> moms = MomentsFromPH(a, A, 5);
>>> disp(moms);
      0.20939      0.10449     0.089092      0.11027      0.17953
>>> [a, A] = MEFromMoments(moms);
>>> disp(a);
      0.33333      0.33333      0.33333
>>> disp(A);
       -8.085       10.177      -9.9999
      -1.2584      -5.1438       1.7873
      -1.9255       1.9599      -4.9712
>>> memoms = MomentsFromME(a, A, 5);
>>> disp(memoms);
      0.20939      0.10449     0.089092      0.11027      0.17953

For Mathematica:

>>> a = {0.1,0.9,0};
>>> A = {{-6.2, 2, 0},{2, -9, 1},{1, 0, -3}};
>>> moms = MomentsFromPH[a, A, 5];
>>> Print[moms];
{0.20938722294654497, 0.10448912014333092, 0.08909150039190732, 0.11026674096545433, 0.179530273247209}
>>> {a, A} = MEFromMoments[moms];
>>> Print[a];
{1/3, 1/3, 1/3}
>>> Print[A];
{{-8.084991901863543, 10.176612950254244, -9.999939852873878},
 {-1.2584436954049303, -5.143808678565172, 1.7873056877319793},
 {-1.925450036434008, 1.959914946726235, -4.971199419570917}}
>>> memoms = MomentsFromME[a, A, 5];
>>> Print[memoms];
{0.209387222946545, 0.10448912014333095, 0.08909150039190736, 0.11026674096545445, 0.17953027324720922}

For Python/Numpy:

>>> a = ml.matrix([[0.1,0.9,0]])
>>> A = ml.matrix([[-6.2, 2, 0],[2, -9, 1],[1, 0, -3]])
>>> moms = MomentsFromPH(a, A, 5)
>>> print(moms)
[0.20938722294654497, 0.10448912014333091, 0.089091500391907288, 0.11026674096545433, 0.17953027324720897]
>>> a, A = MEFromMoments(moms)
>>> print(a)
[[ 0.33333  0.33333  0.33333]]
>>> print(A)
[[ -8.08499  10.17661  -9.99994]
 [ -1.25844  -5.14381   1.78731]
 [ -1.92545   1.95991  -4.9712 ]]
>>> memoms = MomentsFromME(a, A, 5)
>>> print(memoms)
[0.20938722294654494, 0.10448912014333089, 0.089091500391907275, 0.11026674096545437, 0.1795302732472091]