`central_moment`

Calculates the central moment.

Syntax


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central_moment(x, k)

Description


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m = central_moment(x, k)

Compute the k-th central moment of all the observations.

That is,

b_{k} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{k}

$x_i,i=1,2,\cdots,n$ $i$ -th observed value, and

\bar{x} = \frac{1}{n} \sum_{i}^{n} x_{i}

Examples


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>>> from OpenHA.processing.feature import central_moment
>>> import numpy as np

>>> x = np.array([0, 1, 2, 3, 4])
>>> print(central_moment(x, 2))

# x_ = 2
# = ((-2)^2 + 1^2 + 0^2 + 1^2 + 2^2) / 5
# = (4 + 1 + 0 + 1 + 4) / 5
# = 10 / 5
2

Input Arguments

x —— The value of observations, specified as an array of N-D array of length n.

For an n-by-m array, it indicates n observations with m features.

k —— Order of raw moment, specified as a positive integer scalar.

Properties of Arguments

Name of the parameters	Is optional?	Source, dialog or input port?
`x`	No	Input port
`k`	No	Dialog