butools.dph.PmfFromDPH¶

butools.dph.PmfFromDPH()¶

Matlab:	pmf = PmfFromDPH(alpha, A, x, prec)
Mathematica:	pmf = PmfFromDPH[alpha, A, x, prec]
Python/Numpy:	pmf = PmfFromDPH(alpha, A, x, prec)

Returns the probability mass function 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. x : vector of non-negative integers The density function will be computed at these points prec : double, optional Numerical precision to check if the input DPH distribution is valid. The default value is 1e-14.

Returns:

pmf : column vector of doubles The probabilities that the discrete phase type distributed random variable takes the corresponding “x” values

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];
>>> x = (0.0:1.0:1000.0);
>>> pmf = PmfFromDPH(a, A, x);
>>> plot(x, pmf)

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}};
>>> x = Range[0.0,1000.0,1.0];
>>> pmf = PmfFromDPH[a, A, x];
>>> ListLinePlot[{Transpose[{x, pmf}]}]

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]])
>>> x = np.arange(0.0,1001.0,1.0)
>>> pmf = PmfFromDPH(a, A, x)
>>> plt.plot(x, pmf)