butools.dph.DPH3From5Moments¶

butools.dph.DPH3From5Moments()¶

Matlab:	`[alpha, A] = DPH3From5Moments(moms, prec)`
Mathematica:	`{alpha, A} = DPH3From5Moments[moms, prec]`
Python/Numpy:	`alpha, A = DPH3From5Moments(moms, prec)`

Returns an order-3 discrete phase-type distribution which has the same 5 moments as given.

Parameters:

moms : vector of doubles, length(5)

The moments to match

prec : double, optional

Numerical precision, default value is 1e-14

Returns:

alpha : matrix, shape (1,3)

The initial probability vector of the DPH(3)

A : matrix, shape (3,3)

Transition probability matrix of the DPH(3)

Notes

Raises an error if the moments are not feasible with a DPH(3).

This procedure first calls ‘MGFromMoments’, then transforms it to DPH(3) by ‘CanonicalFromDPH3’.

Examples

For Matlab:

>>> a = [0.7,0.1,0.2];
>>> A = [0.2, 0.51, 0.1; 0.58, 0.41, 0; 0.1, 0.4, 0.3];
>>> moms = MomentsFromDPH(a, A);
>>> disp(moms);
       9.3096        175.1       4968.7   1.8805e+05   8.8966e+06
>>> [b, B] = DPH3From5Moments(moms);
>>> disp(b);
      0.73989     0.076837      0.18327
>>> disp(B);
      0.89971      0.10029            0
            0     0.010293      0.98971
            0     0.050581            0
>>> phmoms = MomentsFromMG(b, B, 5);
>>> disp(phmoms);
       9.3096        175.1       4968.7   1.8805e+05   8.8966e+06

For Mathematica:

>>> a = {0.7,0.1,0.2};
>>> A = {{0.2, 0.51, 0.1},{0.58, 0.41, 0},{0.1, 0.4, 0.3}};
>>> moms = MomentsFromDPH[a, A];
>>> Print[moms];
{9.3096349745331, 175.10327171027384, 4968.663522150066, 188050.43861214988, 8.896632715174045*^6}
>>> {b, B} = DPH3From5Moments[moms];
"Ordered eigenvalues:"{0.8997069306212445, 0.22894830561223567, -0.21865523626858424}
>>> Print[b];
{0.7398925149830309, 0.07683743218204545, 0.18327005283492365}
>>> Print[B];
{{0.8997069306212445, 0.10029306937875548, 0},
 {0, 0.010293069343651429, 0.9897069306563486},
 {0, 0.05058138354526465, 0}}
>>> phmoms = MomentsFromMG[b, B, 5];
>>> Print[phmoms];
{9.309634974533111, 175.10327171027419, 4968.66352215008, 188050.43861215067, 8.89663271517409*^6}

For Python/Numpy:

>>> a = ml.matrix([[0.7,0.1,0.2]])
>>> A = ml.matrix([[0.2, 0.51, 0.1],[0.58, 0.41, 0],[0.1, 0.4, 0.3]])
>>> moms = MomentsFromDPH(a, A)
>>> print(moms)
[9.3096349745331022, 175.10327171027393, 4968.6635221500701, 188050.43861215009, 8896632.7151740566]
>>> b, B = DPH3From5Moments(moms)
>>> print(b)
[[ 0.73989  0.07684  0.18327]]
>>> print(B)
[[ 0.89971  0.10029  0.     ]
 [ 0.       0.01029  0.98971]
 [ 0.       0.05058  0.     ]]
>>> phmoms = MomentsFromMG(b, B, 5)
>>> print(phmoms)
[9.3096349745330773, 175.10327171027262, 4968.6635221500082, 188050.4386121468, 8896632.7151738554]