butools.dph.DPH2From3Moments¶

butools.dph.DPH2From3Moments()¶

Matlab:	[alpha, A] = DPH2From3Moments(moms, prec)
Mathematica:	{alpha, A} = DPH2From3Moments[moms, prec]
Python/Numpy:	alpha, A = DPH2From3Moments(moms, prec)

Returns an order-2 discrete phase-type distribution 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 DPH(2) A : matrix, shape (2,2) Transition probability matrix of the DPH(2)

Notes

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

This procedure first calls ‘MGFromMoments’, then transforms it to DPH(2) by ‘CanonicalFromDPH2’.

Examples

For Matlab:

>>> a = [0.9,0.1];
>>> A = [0.2, 0.61; 0.58, 0.41];
>>> moms = MomentsFromDPH(a, A);
>>> disp(moms);
       10.305       215.13       6764.2
>>> [b, B] = DPH2From3Moments(moms);
>>> disp(b);
      0.43249      0.56751
>>> disp(B);
         0.61         0.39
      0.69692            0
>>> phmoms = MomentsFromDPH(b, B, 3);
>>> disp(phmoms);
       10.305       215.13       6764.2

For Mathematica:

>>> a = {0.9,0.1};
>>> A = {{0.2, 0.61},{0.58, 0.41}};
>>> moms = MomentsFromDPH[a, A];
>>> Print[moms];
{10.304568527918775, 215.1328300136563, 6764.166152521255}
>>> {b, B} = DPH2From3Moments[moms];
>>> Print[b];
{0.43248730964467125, 0.5675126903553286}
>>> Print[B];
{{0.6100000000000014, 0.38999999999999857},
 {0.6969230769230763, 0}}
>>> phmoms = MomentsFromDPH[b, B, 3];
>>> Print[phmoms];
{10.304568527918788, 215.13283001365693, 6764.166152521286}

For Python/Numpy:

>>> a = ml.matrix([[0.9,0.1]])
>>> A = ml.matrix([[0.2, 0.61],[0.58, 0.41]])
>>> moms = MomentsFromDPH(a, A)
>>> print(moms)
[10.304568527918775, 215.1328300136563, 6764.1661525212548]
>>> b, B = DPH2From3Moments(moms)
>>> print(b)
[[ 0.43249  0.56751]]
>>> print(B)
[[ 0.61     0.39   ]
 [ 0.69692  0.     ]]
>>> phmoms = MomentsFromDPH(b, B, 3)
>>> print(phmoms)
[10.304568527918779, 215.1328300136565, 6764.1661525212639]