butools.ph.PdfFromPH¶

butools.ph.PdfFromPH()¶

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

Returns the probability density function of a continuous phase-type distribution.

Parameters:	alpha : vector, shape (1,M) The initial probability vector of the phase-type distribution. A : matrix, shape (M,M) The transient generator matrix of the phase-type distribution. x : vector of doubles The density function will be computed at these points prec : double, optional Numerical precision to check if the input ME distribution is valid. The default value is 1e-14.
Returns:	pdf : column vector of doubles The values of the density function at the corresponding “x” values

Examples

For Matlab:

>>> a = [0.1,0.9,0];
>>> A = [-6.2, 2, 0; 2, -9, 1; 1, 0, -3];
>>> x = (0.0:0.002:3.0);
>>> pdf = PdfFromPH(a, A, x);
>>> plot(x, pdf)

For Mathematica:

>>> a = {0.1,0.9,0};
>>> A = {{-6.2, 2, 0},{2, -9, 1},{1, 0, -3}};
>>> x = Range[0.0,3.0,0.002];
>>> pdf = PdfFromPH[a, A, x];
>>> ListLinePlot[{Transpose[{x, pdf}]}]

For Python/Numpy:

>>> a = ml.matrix([[0.1,0.9,0]])
>>> A = ml.matrix([[-6.2, 2, 0],[2, -9, 1],[1, 0, -3]])
>>> x = np.arange(0.0,3.002,0.002)
>>> pdf = PdfFromPH(a, A, x)
>>> plt.plot(x, pdf)