butools.ph.APH2ndMomentLowerBound¶

butools.ph.APH2ndMomentLowerBound()¶

Matlab:	m2 = APH2ndMomentLowerBound(m1, n)
Mathematica:	m2 = APH2ndMomentLowerBound[m1, n]
Python/Numpy:	m2 = APH2ndMomentLowerBound(m1, n)

Returns the lower bound of the second moment of acyclic phase-type (APH) distributions of order n.

Parameters:	m1 : double The first moment n : int Number of states
Returns:	m2 : double The lowest second moment an order-n APH can have with the given first moment.

References

[R1]	M. Telek and A. Heindl, “Moment bounds for acyclic discrete and continuous phase-type distributions of second order,” in In Proc. of UK Performance Evaluation Workshop, UKPEW, 2002”

Examples

For Matlab:

>>> mean = 1.9;
>>> n = 4;
>>> mom2 = APH2ndMomentLowerBound(mean, n);
>>> disp(mom2);
       4.5125
>>> cv2 = mom2/mean^2-1;
>>> disp(1/cv2);
     4

For Mathematica:

>>> mean = 1.9;
>>> n = 4;
>>> mom2 = APH2ndMomentLowerBound[mean, n];
>>> Print[mom2];
4.5125
>>> cv2 = mom2/mean^2-1;
>>> Print[1/cv2];
3.9999999999999964

For Python/Numpy:

>>> mean = 1.9
>>> n = 4
>>> mom2 = APH2ndMomentLowerBound(mean, n)
>>> print(mom2)
4.5125
>>> cv2 = mom2/mean**2-1
>>> print(1/cv2)
4.0