butools.ph.IntervalPdfFromPH¶

butools.ph.IntervalPdfFromPH()¶

Matlab:	[x,y] = IntervalPdfFromPH(alpha, A, intBounds, prec)
Mathematica:	{x,y} = IntervalPdfFromPH[alpha, A, intBounds, prec]
Python/Numpy:	x, y = IntervalPdfFromPH(alpha, A, intBounds, prec)

Returns the approximate probability density function of a continuous phase-type distribution, based on the probability of falling into intervals.

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. intBounds : vector, shape (K) The array of interval boundaries. The pdf is the probability of falling into an interval divided by the interval length. If the size of intBounds is K, the size of the result is K-1. prec : double, optional Numerical precision to check if the input is a valid phase-type distribution. The default value is 1e-14

Returns:

x : matrix of doubles, shape(K-1,1) The points at which the pdf is computed. It holds the center of the intervals defined by intBounds. y : matrix of doubles, shape(K-1,1) The values of the density function at the corresponding “x” values

Notes

This method is more suitable for comparisons with empirical density functions than the exact one (given by PdfFromPH).

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);
>>> [x, y] = IntervalPdfFromPH(a, A, x);
>>> plot(x, y)

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];
>>> {x, y} = IntervalPdfFromPH[a, A, x];
>>> ListLinePlot[{Transpose[{x, y}]}]

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)
>>> x, y = IntervalPdfFromPH(a, A, x)
>>> plt.plot(x, y)