`kurtosis`

Compute the kurtosis.

Syntax


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kurtosis(x)

Description


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m = kurtosis(x)

$X$ , its kurtosis is,

kurtosis = \frac{E [{(X - μ)}^{4}]}{σ^{4}}

$\mu = E\left(X\right)$ $\sigma = \sqrt{D\left(X\right)}$ .

And its observation is

kurtosis = \sum_{i = 1}^{n} \frac{{(x_{i} - \bar{x})}^{4}}{n} \frac{1}{s^{4}}

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

\bar{x} = \frac{1}{n} \sum_{i}^{n} x_{i}, s = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - \bar{x})}

Examples


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

# normal distribution
>>> x = np.random.randn(1000)
>>> print(kurtosis(x))

2.968569898977294

Input Arguments

x —— A N-D array of observations.

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

Properties of Arguments

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

References

[1] "Measures of Skewness and Kurtosis," Online, https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm.