Source code for simplestatistics.statistics.error_function

from .standard_deviation import standard_deviation
import math

[docs]def error_function(x, decimals = 2): """ The error function, or `Gauss error function`_. .. _`Gauss error function`: https://en.wikipedia.org/wiki/Error_function The function returns the probability that a value in a normal distribution is between :math:`\\frac{x}{sd\\sqrt{2}}` and :math:`\\frac{-x}{sd\\sqrt{2}}`. This implementation is closely modeled after the impementation in `simple-statistics <https://github.com/simple-statistics/simple-statistics>`_, and returns a numerical approximation of the exact value. Args: x: A numerical object denoting sd decimals: number of decimal points (default is 2) Returns: Probability between 0 and 1. Examples: >>> error_function(1) 0.84 >>> error_function(.8, decimals = 1) 0.7 >>> error_function(1.01) 0.85 >>> error_function(-0.4) -0.43 >>> error_function('.75') Traceback (most recent call last): ... ValueError: error_function() only accepts values of type int or float. """ if type(x) not in [int, float]: raise ValueError('error_function() only accepts values of type int or float.') t = 1 / (1 + (0.5 * abs(x))) tau = t * math.exp( (math.pow(x, 2) * - 1) - \ 1.26551223 + \ 1.00002368 * t + \ 0.37409196 * math.pow(t, 2) + \ 0.09678418 * math.pow(t, 3) - \ 0.18628806 * math.pow(t, 4) + \ 0.27886807 * math.pow(t, 5) - \ 1.13520398 * math.pow(t, 6) + \ 1.48851587 * math.pow(t, 7) - \ 0.82215223 * math.pow(t, 8) + \ 0.17087277 * math.pow(t, 9)) if x >= 0: return(round(1 - tau, decimals)) else: return(round(tau - 1, decimals))