butools.moments.FactorialMomsFromMoms¶

butools.moments.FactorialMomsFromMoms()¶

Matlab:	fm = FactorialMomsFromMoms(m)
Mathematica:	fm = FactorialMomsFromMoms[m]
Python/Numpy:	fm = FactorialMomsFromMoms(m)

Returns the factorial moments given the raw moments.

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

The factorial moments are: \(f_i=E(\mathcal{X}(\mathcal{X}-1)\cdots(\mathcal{X}-i+1))\)

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

References

http://en.wikipedia.org/wiki/Factorial_moment

Examples

For Matlab:

>>> M = [1.3, 2.4, 6.03, 20.5, 89.5, 474.9];
>>> fmoms = FactorialMomsFromMoms(M);
>>> disp(fmoms);
          1.3          1.1         1.43         2.92         6.75        19.75
>>> moms = MomsFromFactorialMoms(fmoms);
>>> disp(moms);
          1.3          2.4         6.03         20.5         89.5        474.9
>>> err = norm(moms-M);
>>> disp(err);
   3.5527e-15

For Mathematica:

>>> M = {1.3, 2.4, 6.03, 20.5, 89.5, 474.9};
>>> fmoms = FactorialMomsFromMoms[M];
>>> Print[fmoms];
{1.3, 1.0999999999999999, 1.4300000000000006, 2.919999999999998, 6.750000000000014, 19.75}
>>> moms = MomsFromFactorialMoms[fmoms];
>>> Print[moms];
{1.3, 2.4, 6.03, 20.5, 89.5, 474.9}
>>> err = Norm[moms-M];
>>> Print[err];
0.

For Python/Numpy:

>>> M = [1.3, 2.4, 6.03, 20.5, 89.5, 474.9]
>>> fmoms = FactorialMomsFromMoms(M)
>>> print(fmoms)
[1.3, 1.0999999999999999, 1.4300000000000006, 2.9199999999999982, 6.7500000000000142, 19.75]
>>> moms = MomsFromFactorialMoms(fmoms)
>>> print(moms)
[1.3, 2.3999999999999999, 6.0300000000000002, 20.5, 89.5, 474.89999999999998]
>>> err = la.norm(np.array(moms)-np.array(M))
>>> print(err)
0.0