butools.dph.PmfFromMG¶

butools.dph.PmfFromMG()¶

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

Returns the probability mass function of a matrix- geometric distribution.

Parameters:

alpha : vector, shape (1,M) The initial vector of the matrix-geometric distribution. The sum of the entries of pi0 is less or equal to 1. A : matrix, shape (M,M) The matrix parameter of the matrix-geometric 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 MG distribution is valid. The default value is 1e-14.

Returns:

pmf : column vector of doubles The probabilities that the matrix-geometrically distributed random variable takes the corresponding “x” values

Examples

For Matlab:

>>> a = [-0.6,0.3,1.3];
>>> A = [0.25, 0.2, -0.15; 0.3, 0.1, 0.25; 0, 0.2, 0.47];
>>> x = (0.0:1.0:100.0);
>>> pmf = PmfFromMG(a, A, x);
>>> plot(x, pmf)

For Mathematica:

>>> a = {-0.6,0.3,1.3};
>>> A = {{0.25, 0.2, -0.15},{0.3, 0.1, 0.25},{0, 0.2, 0.47}};
>>> x = Range[0.0,100.0,1.0];
>>> pmf = PmfFromMG[a, A, x];
>>> ListLinePlot[{Transpose[{x, pmf}]}]

For Python/Numpy:

>>> a = ml.matrix([[-0.6,0.3,1.3]])
>>> A = ml.matrix([[0.25, 0.2, -0.15],[0.3, 0.1, 0.25],[0, 0.2, 0.47]])
>>> x = np.arange(0.0,101.0,1.0)
>>> pmf = PmfFromMG(a, A, x)
>>> plt.plot(x, pmf)