butools.ph.MEOrderFromMoments¶

butools.ph.MEOrderFromMoments()¶

Matlab:	order = MEOrderFromMoments(moms, prec)
Mathematica:	order = MEOrderFromMoments[moms, prec]
Python/Numpy:	order = MEOrderFromMoments(moms, prec)

Returns the order of ME distribution that can realize the given moments.

Parameters:	moms : list of doubles The list of moments prec : double, optional Precision used to detect if the determinant of the Hankel matrix is zero. The default value is 1e-12.
Returns:	order : int The order of ME distribution that can realize the given moments

References

[R25]

L. Bodrog, A. Horvath, M. Telek, “Moment characterization of matrix exponential and Markovian arrival processes,” Annals of Operations Research, vol. 160, pp. 51-68, 2008.

Examples

For Matlab:

>>> a = [0.1,0.9,0];
>>> A = [-6.2, 2., 0.; 2., -9., 1.; 1., 0., -3.];
>>> moms = MomentsFromME(a, A);
>>> disp(moms);
      0.20939      0.10449     0.089092      0.11027      0.17953
>>> mo = MEOrderFromMoments(moms);
>>> disp(mo);
     3
>>> b = [0.2,0.3,0.5];
>>> B = [-1., 0., 0.; 0., -3., 2.; 0., -2., -3.];
>>> [a, A] = MonocyclicPHFromME(b, B);
>>> moms = MomentsFromME(a, A);
>>> disp(moms);
  Columns 1 through 6
      0.35385      0.41893       1.1552       4.6998       23.838       143.78
  Columns 7 through 12
       1007.8       8064.3        72578   7.2577e+05   7.9834e+06     9.58e+07
  Columns 13 through 18
   1.2454e+09   1.7436e+10   2.6153e+11   4.1846e+12   7.1137e+13   1.2805e+15
  Columns 19 through 24
   2.4329e+16   4.8658e+17   1.0218e+19    2.248e+20   5.1704e+21   1.2409e+23
  Columns 25 through 30
   3.1022e+24   8.0658e+25   2.1778e+27   6.0978e+28   1.7684e+30   5.3051e+31
  Columns 31 through 36
   1.6446e+33   5.2626e+34   1.7367e+36   5.9047e+37   2.0666e+39   7.4399e+40
  Columns 37 through 42
   2.7528e+42    1.046e+44   4.0796e+45   1.6318e+47   6.6905e+48     2.81e+50
  Columns 43 through 48
   1.2083e+52   5.3165e+53   2.3924e+55   1.1005e+57   5.1725e+58   2.4828e+60
  Columns 49 through 53
   1.2166e+62   6.0828e+63   3.1022e+65   1.6132e+67   8.5498e+68
>>> mo = MEOrderFromMoments(moms);
>>> disp(mo);
     3

For Mathematica:

>>> a = {0.1,0.9,0};
>>> A = {{-6.2, 2., 0.},{2., -9., 1.},{1., 0., -3.}};
>>> moms = MomentsFromME[a, A];
>>> Print[moms];
{0.20938722294654497, 0.10448912014333092, 0.08909150039190732, 0.11026674096545433, 0.179530273247209}
>>> mo = MEOrderFromMoments[moms];
>>> Print[mo];
3
>>> b = {0.2,0.3,0.5};
>>> B = {{-1., 0., 0.},{0., -3., 2.},{0., -2., -3.}};
>>> {a, A} = MonocyclicPHFromME[b, B];
>>> moms = MomentsFromME[a, A];
>>> Print[moms];
{0.3538461538461526, 0.4189349112425999, 1.1552116522530596, 4.69983543993552, 23.83775616561553, 143.78185836646747, 1007.8194071104357, 8064.27288252136, 72578.13371878403, 725767.9587461551, 7.983382351398367*^6, 9.5800362980475*^7, 1.2454041496660538*^9, 1.7435657571499924*^10, 2.6153486913885196*^11, 4.184557956997617*^12, 7.113748555089039*^13, 1.2804747410630338*^15, 2.4329020082839036*^16, 4.8658040164763456*^17, 1.0218188434426337*^19, 2.248001455559376*^20, 5.17040334777803*^21, 1.2408968034663935*^23, 3.10224200866599*^24, 8.065829222531742*^25, 2.17777389008359*^27, 6.0977668922340655*^28, 1.7683523987478783*^30, 5.305057196243631*^31, 1.644567730835523*^33, 5.262616738673672*^34, 1.7366635237623102*^36, 5.904655980791849*^37, 2.066629593277145*^39, 7.4398665357977185*^40, 2.7527506182451524*^42, 1.046045234933157*^44, 4.079576416239309*^45, 1.6318305664957217*^47, 6.690505322632454*^48, 2.8100122355056267*^50, 1.2083052612674186*^52, 5.316543149576638*^53, 2.392444417309483*^55, 1.1005244319623617*^57, 5.172464830223095*^58, 2.4827831185070832*^60, 1.2165637280684694*^62, 6.082818640342342*^63, 3.1022375065745914*^65, 1.613163503418786*^67, 8.549766568119559*^68}
>>> mo = MEOrderFromMoments[moms];
>>> Print[mo];
3

For Python/Numpy:

>>> a = ml.matrix([[0.1,0.9,0]])
>>> A = ml.matrix([[-6.2, 2., 0.],[2., -9., 1.],[1., 0., -3.]])
>>> moms = MomentsFromME(a, A)
>>> print(moms)
[0.20938722294654497, 0.10448912014333091, 0.089091500391907288, 0.11026674096545433, 0.17953027324720897]
>>> mo = MEOrderFromMoments(moms)
>>> print(mo)
3
>>> b = ml.matrix([[0.2,0.3,0.5]])
>>> B = ml.matrix([[-1., 0., 0.],[0., -3., 2.],[0., -2., -3.]])
>>> a, A = MonocyclicPHFromME(b, B)
>>> moms = MomentsFromME(a, A)
>>> print(moms)
[0.35384615384615531, 0.41893491124260573, 1.155211652253076, 4.699835439935578, 23.83775616561579, 143.78185836646887, 1007.8194071104439, 8064.272882521419, 72578.133718784462, 725767.95874615829, 7983382.3513983944, 95800362.980475202, 1245404149.6660547, 17435657571.499924, 261534869138.85153, 4184557956997.604, 71137485550890.109, 1280474741063026.2, 24329020082838864.0, 4.8658040164763066e+17, 1.021818843442624e+19, 2.248001455559353e+20, 5.17040334777797e+21, 1.2408968034663769e+23, 3.1022420086659455e+24, 8.065829222531619e+25, 2.1777738900835537e+27, 6.0977668922339555e+28, 1.7683523987478442e+30, 5.305057196243521e+31, 1.6445677308354878e+33, 5.262616738673549e+34, 1.7366635237622677e+36, 5.904655980791697e+37, 2.066629593277089e+39, 7.439866535797508e+40, 2.752750618245071e+42, 1.0460452349331244e+44, 4.0795764162391765e+45, 1.6318305664956671e+47, 6.690505322632222e+48, 2.810012235505527e+50, 1.2083052612673737e+52, 5.316543149576433e+53, 2.392444417309389e+55, 1.1005244319623167e+57, 5.172464830222877e+58, 2.4827831185069758e+60, 1.2165637280684155e+62, 6.082818640342062e+63, 3.1022375065744455e+65, 1.613163503418708e+67, 8.549766568119135e+68]
>>> mo = MEOrderFromMoments(moms)
>>> print(mo)
3