butools.dph.MomentsFromDPH¶

butools.dph.MomentsFromDPH()¶

Matlab:	moms = MomentsFromDPH(alpha, A, K, prec)
Mathematica:	moms = MomentsFromDPH[alpha, A, K, prec]
Python/Numpy:	moms = MomentsFromDPH(alpha, A, K, prec)

Returns the first K moments of a discrete phase-type distribution.

Parameters:

alpha : vector, shape (1,M) The initial probability vector of the discrete phase- type distribution. The sum of the entries of pi0 is less or equal to 1. A : matrix, shape (M,M) The transient generator matrix of the discrete phase- type distribution. K : int, optional Number of moments to compute. If K=0, 2*M-1 moments are computed. The default value is 0. prec : double, optional Numerical precision for checking the input. The default value is 1e-14.

Returns:

moms : row vector of doubles The vector of moments.

Examples

For Matlab:

>>> a = [0.76,0,0.24];
>>> A = [0.34, 0.66, 0; 0.79, 0.05, 0.07; 0.26, 0.73, 0.01];
>>> moms = MomentsFromDPH(a, A, 5);
>>> disp(moms);
       26.995         1398   1.0853e+05   1.1233e+07   1.4533e+09

For Mathematica:

>>> a = {0.76,0,0.24};
>>> A = {{0.34, 0.66, 0},{0.79, 0.05, 0.07},{0.26, 0.73, 0.01}};
>>> moms = MomentsFromDPH[a, A, 5];
>>> Print[moms];
{26.995340611502304, 1397.9993695881547, 108525.47866809377, 1.1232963460675944*^7, 1.4533393399621515*^9}

For Python/Numpy:

>>> a = ml.matrix([[0.76,0,0.24]])
>>> A = ml.matrix([[0.34, 0.66, 0],[0.79, 0.05, 0.07],[0.26, 0.73, 0.01]])
>>> moms = MomentsFromDPH(a, A, 5)
>>> print(moms)
[26.995340611502307, 1397.9993695881547, 108525.47866809377, 11232963.460675946, 1453339339.9621518]