butools.ph.CdfFromME¶

butools.ph.CdfFromME()¶

Matlab:	cdf = CdfFromME(alpha, A, x)
Mathematica:	cdf = CdfFromME[alpha, A, x]
Python/Numpy:	cdf = CdfFromME(alpha, A, x)

Returns the cummulative distribution function of a matrix-exponential distribution.

Parameters:	alpha : matrix, shape (1,M) The initial vector of the matrix-exponential distribution. A : matrix, shape (M,M) The matrix parameter of the matrix-exponential distribution. x : vector of doubles The cdf will be computed at these points
Returns:	cdf : column vector of doubles The values of the cdf at the corresponding “x” values

Examples

For Matlab:

>>> a = [0.2,0.3,0.5];
>>> A = [-1, 0, 0; 0, -3, 2; 0, -2, -3];
>>> x = (0.0:0.01:5.0);
>>> cdf = CdfFromME(a, A, x);
>>> plot(x, cdf)

For Mathematica:

>>> a = {0.2,0.3,0.5};
>>> A = {{-1, 0, 0},{0, -3, 2},{0, -2, -3}};
>>> x = Range[0.0,5.0,0.01];
>>> cdf = CdfFromME[a, A, x];
>>> ListLinePlot[{Transpose[{x, cdf}]}]

For Python/Numpy:

>>> a = ml.matrix([[0.2,0.3,0.5]])
>>> A = ml.matrix([[-1, 0, 0],[0, -3, 2],[0, -2, -3]])
>>> x = np.arange(0.0,5.01,0.01)
>>> cdf = CdfFromME(a, A, x)
>>> plt.plot(x, cdf)