butools.ph.PH2From3Moments¶

butools.ph.PH2From3Moments()¶

Matlab:	`[alpha, A] = PH2From3Moments(moms, prec)`
Mathematica:	`{alpha, A} = PH2From3Moments[moms, prec]`
Python/Numpy:	`alpha, A = PH2From3Moments(moms, prec)`

Returns a PH(2) which has the same 3 moments as given.

Parameters:

moms : vector of doubles, length(3)

The moments to match

prec : double, optional

Numerical precision, default value is 1e-14

Returns:

alpha : matrix, shape (1,2)

The initial probability vector of the PH(2)

A : matrix, shape (2,2)

Transient generator matrix of the PH(2)

Notes

Raises an error if the moments are not feasible with a PH(2).

References

[R39]

M. Telek and A. Heindl, “Moment bounds for acyclic discrete and continuous phase-type distributions of second order,” in In Proc. of UK Performance Evaluation Workshop, UKPEW, 2002”

Examples

For Matlab:

>>> moms = [10.0, 160.0, 3500.0];
>>> [a, A] = PH2From3Moments(moms);
>>> disp(a);
       0.8702       0.1298
>>> disp(A);
     -0.15576      0.15576
            0     -0.22659
>>> phmoms = MomentsFromPH(a, A, 3);
>>> disp(phmoms);
          10         160        3500
>>> moms = [10.0, 260.0, 13500.0];
>>> [a, A] = PH2From3Moments(moms);
>>> disp(a);
     0.090975      0.90902
>>> disp(A);
    -0.041955     0.041955
            0     -0.12769
>>> phmoms = MomentsFromPH(a, A, 3);
>>> disp(phmoms);
           10          260        13500

For Mathematica:

>>> moms = {10.0, 160.0, 3500.0};
>>> {a, A} = PH2From3Moments[moms];
>>> Print[a];
{0.8701999867127262, 0.12980001328727375}
>>> Print[A];
{{-0.15576001594472852, 0.15576001594472852},
 {0, -0.22659292523174202}}
>>> phmoms = MomentsFromPH[a, A, 3];
>>> Print[phmoms];
{10.000000000000002, 160.00000000000006, 3500.0000000000023}
>>> moms = {10.0, 260.0, 13500.0};
>>> {a, A} = PH2From3Moments[moms];
>>> Print[a];
{0.09097530055983008, 0.90902469944017}
>>> Print[A];
{{-0.04195498612800784, 0.04195498612800784},
 {0, -0.1276878710148493}}
>>> phmoms = MomentsFromPH[a, A, 3];
>>> Print[phmoms];
{10., 260.00000000000006, 13500.000000000005}

For Python/Numpy:

>>> moms = [10.0, 160.0, 3500.0]
>>> a, A = PH2From3Moments(moms)
>>> print(a)
[[ 0.8702  0.1298]]
>>> print(A)
[[-0.15576  0.15576]
 [ 0.      -0.22659]]
>>> phmoms = MomentsFromPH(a, A, 3)
>>> print(phmoms)
[10.0, 160.0, 3500.0]
>>> moms = [10.0, 260.0, 13500.0]
>>> a, A = PH2From3Moments(moms)
>>> print(a)
[[ 0.09098  0.90902]]
>>> print(A)
[[-0.04195  0.04195]
 [ 0.      -0.12769]]
>>> phmoms = MomentsFromPH(a, A, 3)
>>> print(phmoms)
[10.0, 260.00000000000006, 13500.000000000005]