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Skewness

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Skewness[data]

gives the coefficient of skewness (a measure of asymmetry) of data, equivalent to CentralMoment[data, 3] / CentralMoment[data, 2]^(3/2). For a matrix it is taken columnwise.

Examples (2)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (2)

In[1]:= Skewness[{1, 2, 3, 10}]
Out[1]= 18/25 Sqrt[2]

In[2]:= Skewness[{1., 2., 3., 4., 5.}]
Out[2]= 0.0

Algorithm

skewness.c -- Skewness[]. Split from stats.c; see stats.h and stats_common.h for the subsystem layout.

Skewness[data] -- the coefficient of skewness, a measure of asymmetry. Equivalent to CentralMoment[data, 3] / CentralMoment[data, 2]^(3/2). For a matrix or array it is taken columnwise (the CentralMoment ratio threads). The shared body lives in stats_common.c (stats_standardized_moment), which also routes NDArray / packed inputs to the buffer kernel ndred_skewness.

Implementation notes

  • Protected.
  • Equivalent to CentralMoment[data, 3] / CentralMoment[data, 2]^(3/2).
  • For a matrix, gives the columnwise skewnesses.
  • Handles numerical and symbolic data; exact input gives exact output (a radical in general).
  • Fast path on NDArray/packed real buffers (ndred_skewness) and lowerable inside Compile[]; an integer buffer degrades to the exact List result.

Attributes: Protected.

References

See also: NDArray, List