Source code for calculus.stats.moment

# -*- coding: UTF-8 -*-
:author:   Brigitte Bigi
:summary:  A collection of basic statistical functions for python.

.. _This file is part of SPPAS:

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    Copyright (C) 2011-2021  Brigitte Bigi
    Laboratoire Parole et Langage, Aix-en-Provence, France

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from .central import fmean
from .variability import lstdev

# ----------------------------------------------------------------------------

[docs]def lmoment(items, moment=1): """Calculate the r-th moment about the mean for a sample. 1/n * SUM((items(i)-mean)**r) :param items: (list) list of data values :param moment: :returns: (float) """ if moment == 1: return 0. mn = fmean(items) momentlist = [(i-mn)**moment for i in items] return sum(momentlist) / float(len(items))
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[docs]def lvariation(items): """Calculate the coefficient of variation of data values. It shows the extent of variability in relation to the mean. It's a standardized measure of dispersion: stdev / mean and returned as a percentage. :param items: (list) list of data values :returns: (float) """ m = float(fmean(items)) if m == 0.: return 0. return lstdev(items) / float(fmean(items)) * 100.
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[docs]def lskew(items): """Calculate the skewness of a distribution. The skewness represents a measure of the asymmetry: an understanding of the skewness of the dataset indicates whether deviations from the mean are going to be positive or negative. :param items: (list) list of data values :returns: (float) """ return lmoment(items, 3) / pow(lmoment(items, 2), 1.5)
# ---------------------------------------------------------------------------
[docs]def lkurtosis(items): """Return the kurtosis of a distribution. The kurtosis represents a measure of the "peakedness": a high kurtosis distribution has a sharper peak and fatter tails, while a low kurtosis distribution has a more rounded peak and thinner tails. :param items: (list) list of data values :returns: (float) """ return lmoment(items, 4) / pow(lmoment(items, 2), 2.0)