butools.moments.NormMomsFromMoms¶

butools.moments.NormMomsFromMoms()¶

Matlab:	nm = NormMomsFromMoms(m)
Mathematica:	nm = NormMomsFromMoms[m]
Python/Numpy:	nm = NormMomsFromMoms(m)

Returns the normalized moments given the raw moments.

The raw moments are: \(m_i=E(\mathcal{X}^i)\)

The normalized moments are: \(\displaystyle n_i=\frac{m_i}{m_{i-1} m_1}\)

Parameters:	m : vector of doubles The list of raw moments (starting with the first moment)
Returns:	nm : vector of doubles The list of normalized moments

Examples

For Matlab:

>>> M = [1.2, 5., 38., 495., 9215.];
>>> nmoms = NormMomsFromMoms(M);
>>> disp(nmoms);
          1.2       3.4722       6.3333       10.855       15.513
>>> moms = MomsFromNormMoms(nmoms);
>>> disp(moms);
          1.2            5           38          495         9215
>>> err = norm(moms-M);
>>> disp(err);
     0

For Mathematica:

>>> M = {1.2, 5., 38., 495., 9215.};
>>> nmoms = NormMomsFromMoms[M];
>>> Print[nmoms];
{1.2, 3.4722222222222223, 6.333333333333333, 10.855263157894736, 15.513468013468012}
>>> moms = MomsFromNormMoms[nmoms];
>>> Print[moms];
{1.2, 5., 37.99999999999999, 494.99999999999983, 9214.999999999996}
>>> err = Norm[moms-M];
>>> Print[err];
3.641980348156267*^-12

For Python/Numpy:

>>> M = [1.2, 5., 38., 495., 9215.]
>>> nmoms = NormMomsFromMoms(M)
>>> print(nmoms)
[1.2, 3.4722222222222228, 6.333333333333333, 10.855263157894738, 15.513468013468014]
>>> moms = MomsFromNormMoms(nmoms)
>>> print(moms)
[1.2, 5.000000000000001, 38.00000000000001, 495.00000000000017, 9215.000000000004]
>>> err = la.norm(np.array(moms)-np.array(M))
>>> print(err)
3.641980456457359e-12