Central Moments

Central Moments#

See also Wikipedia [1214]

Calculating the central moments from the factorial moments#

ctx.centralmoments_from_factorialmoments(self, mfac)#

where ctx is ipm, dec, mpm, or gmp.

Calculates the central moments \(\mu_r\) from the factorial moments.

Calculating the central moments from the raw moments#

ctx.centralmoments_from_rawmoments(central, raw)#

where ctx is ipm, dec, mpm, or gmp.

Calculates the central moments \(\mu_r\) from raw the moments \(\mu_r'\) (see Lee and Lin [426], Rinne [505], p. 36):

\[\mu_r = \sum_{j=0}^r \binom{r}{j} \mu'_{r-j} (-\mu'_1)^{j}\]
>>> from mpfunlab import dec, mpr, ivr, ivc
>>> ivr.dps = 25; ivr.pretty = True
>>> ivr.exp([-inf,0])
[0.0, 1.0]
>>> ivr.exp([0,1])
[1.0, 2.71828182845904523536028749558]

Calculating the central moments from the cumulants#

ctx.centralmoments_from_cumulants()#

where ctx is ipm, dec, mpm, or gmp.

Calculates the central moments \(\mu_r\) from the cumulants \(\kappa_r\) (see Lee and Lin [426], Rinne [505], p. 36):

\[\mu_r = \kappa_r + \sum_{j=1}^{r-1} \binom{r-1}{j-1} \mu_{r-j} \kappa_j\]
>>> from mpfunlab import dec, mpr, ivr, ivc
>>> ivr.dps = 25; ivr.pretty = True
>>> ivr.exp([-inf,0])
[0.0, 1.0]
>>> ivr.exp([0,1])
[1.0, 2.71828182845904523536028749558]
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