butools.moments.ReducedMomsFromMoms¶

butools.moments.ReducedMomsFromMoms()¶

Matlab:	rm = ReducedMomsFromMoms(m)
Mathematica:	rm = ReducedMomsFromMoms[m]
Python/Numpy:	rm = ReducedMomsFromMoms(m)

Returns the reduced moments given the raw moments.

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

The reduced moments are: \(\displaystyle r_i=\frac{m_i}{i!}\)

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

Examples

For Matlab:

>>> M = [1.2, 5., 38., 495., 9215.];
>>> rmoms = ReducedMomsFromMoms(M);
>>> disp(rmoms);
          1.2          2.5       6.3333       20.625       76.792
>>> moms = MomsFromReducedMoms(rmoms);
>>> disp(moms);
          1.2            5           38          495         9215
>>> err = norm(moms-M);
>>> disp(err);
     0

For Mathematica:

>>> M = {1.2, 5., 38., 495., 9215.};
>>> rmoms = ReducedMomsFromMoms[M];
>>> Print[rmoms];
{1.2, 2.5, 6.333333333333333, 20.625, 76.79166666666667}
>>> moms = MomsFromReducedMoms[rmoms];
>>> Print[moms];
{1.2, 5., 38., 495., 9215.}
>>> err = Norm[moms-M];
>>> Print[err];
0.

For Python/Numpy:

>>> M = [1.2, 5., 38., 495., 9215.]
>>> rmoms = ReducedMomsFromMoms(M)
>>> print(rmoms)
[1.2, 2.5, 6.333333333333333, 20.625, 76.79166666666667]
>>> moms = MomsFromReducedMoms(rmoms)
>>> print(moms)
[1.2, 5.0, 38.0, 495.0, 9215.0]
>>> err = la.norm(np.array(moms)-np.array(M))
>>> print(err)
0.0