butools.map.MAP2CorrelationBounds¶

butools.map.MAP2CorrelationBounds()¶

Matlab:	[lb, ub] = MAP2CorrelationBounds(moms)
Mathematica:	{lb, ub} = MAP2CorrelationBounds[moms]
Python/Numpy:	lb, ub = MAP2CorrelationBounds(moms)

Returns the upper and lower correlation bounds for a MAP(2) given the three marginal moments.

!!!TO CHECK!!!

Parameters:	moms : vector, length(3) First three marginal moments of the inter-arrival times
Returns:	lb : double Lower correlation bound ub : double Upper correlation bound

References

[R17]

L Bodrog, A Heindl, G Horvath, M Telek, “A Markovian Canonical Form of Second-Order Matrix-Exponential Processes,” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 190:(2) pp. 459-477. (2008)

Examples

For Matlab:

>>> D0 = [-14., 1.; 1., -25.];
>>> D1 = [6., 7.; 3., 21.];
>>> moms = MarginalMomentsFromMAP(D0, D1, 3);
>>> disp(moms);
      0.04918    0.0052609   0.00091819
>>> [lb, ub] = MAP2CorrelationBounds(moms);
>>> disp(lb);
    -0.030588
>>> disp(ub);
     0.074506

For Mathematica:

>>> D0 = {{-14., 1.},{1., -25.}};
>>> D1 = {{6., 7.},{3., 21.}};
>>> moms = MarginalMomentsFromMAP[D0, D1, 3];
>>> Print[moms];
{0.04918032786885247, 0.005260932876133214, 0.0009181867601560783}
>>> {lb, ub} = MAP2CorrelationBounds[moms];
>>> Print[lb];
-0.030588145972596268
>>> Print[ub];
0.0745055540503923

For Python/Numpy:

>>> D0 = ml.matrix([[-14., 1.],[1., -25.]])
>>> D1 = ml.matrix([[6., 7.],[3., 21.]])
>>> moms = MarginalMomentsFromMAP(D0, D1, 3)
>>> print(moms)
[0.049180327868852472, 0.005260932876133214, 0.00091818676015607825]
>>> lb, ub = MAP2CorrelationBounds(moms)
>>> print(lb)
-0.0305881459726
>>> print(ub)
0.0745055540504