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Kurtosis

Status: Stable

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

Description

Kurtosis[data]

gives the coefficient of kurtosis (peak/tail vs flank concentration) of data, equivalent to CentralMoment[data, 4] / CentralMoment[data, 2]^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]:= Kurtosis[{1, 2, 3, 4, 5}]
Out[1]= 17/10

In[2]:= Kurtosis[{1, 2, 4, 8}]
Out[2]= 25141/13225

Algorithm

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

Kurtosis[data] -- the coefficient of kurtosis, a measure of peak/tail vs flank concentration. Equivalent to CentralMoment[data, 4] / CentralMoment[data, 2]^2 (Pearson kurtosis, not the excess form). 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_kurtosis.

Implementation notes

  • Protected.
  • Equivalent to CentralMoment[data, 4] / CentralMoment[data, 2]^2 (Pearson kurtosis, not the excess form).
  • For a matrix, gives the columnwise kurtoses.
  • Handles numerical and symbolic data; exact input gives exact output.
  • Fast path on NDArray/packed real buffers (ndred_kurtosis) and lowerable inside Compile[]; an integer buffer degrades to the exact List result.

Attributes: Protected.

References

See also: NDArray, List