Source code for simplestatistics.statistics.skew

Implements skew() function to calculate skewness of a variable

# I need sane division that returns a float not int
from __future__ import division

from .decimalize import decimalize
from .mean import mean
from .sum import sum # pylint: disable=redefined-builtin

[docs]def skew(x): """ Skew or `Skewness`_ is a measure of the asymmetry of the probability distribution of a variable around its mean. .. _`Skewness`: A positive (+ve) skewness value indicates a long tail to the **right** of the mean. A negative (-ve) skewness value indicates a long tail to the **left** of the mean. There are several equations to calculate skewness. The one used in this function is `Pearson's moment coefficient of skewness`_. .. _`Pearson's moment coefficient of skewness`: \ Equation: .. math:: \\gamma_1 = E\\Bigg[\\bigg(\\frac{(X-\\mu)^3}{\\sigma}\\bigg)\\Bigg] = \\frac{\\mu^3}{\\sigma^3} = \\frac{E[(X - \\mu)^3]}{(E[(X - \\mu)^3])^{3/2}} = \\frac{\\kappa_3}{\\kappa_2^{3/2}} which can be rewritten as .. math:: \\gamma_1 = \\frac{\\frac{1}{n} \\sum(X - \\mu)^3}{\\frac{1}{n} (\\sum(X - \\mu)^2)^{3/2}} Args: x: A list of numerical objects. Returns: A numerical object. Examples: >>> skew([1, 2, 3]) 0.0 >>> skew([1, 2, 5]) 0.5279896038431618 >>> skew([20, 30]) # skew of a variable that contains two observations is always 0 0.0 >>> skew(9) # no skew for a single number/value """ if type(x) in [int, float]: return(None) mean_x = decimalize(mean(x)) n = len(x) m2 = sum([pow((value - mean_x), 2) for value in x]) * (1/n) m3 = sum([pow((value - mean_x), 3) for value in x]) * (1/n) m2_32 = pow(m2, 1.5) return(m3/m2_32)