CDF of Gaussian distribution

The cumulative distribution function (CDF) of Gaussian distribution with standard deviation (sig) and mean (cen) in python

Ref: 

https://www.mathworks.com/help/matlab/ref/erf.html

https://introcs.cs.princeton.edu/java/11gaussian/

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python code:

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from scipy import special

import matplotlib.pyplot as plt

import numpy as np

def erfValue(x, cen, sig):

    #           1                 x - cen

    # erf(x) = --- (1 + erf(-----------------))

    #           2             sqrt(2) * sig

    return 0.5*(1+special.erf((x-cen)/(np.sqrt(2)*sig)))

def erfcValue(x, cen, sig):

    return 1-erfValue(x, cen, sig)

cen = 9.54

sig=2

xx = np.arange(0,20,step=.01)

erf = erfValue(xx, cen, sig)

plt.figure()

plt.plot(xx,erf,'r')

x1 = cen

y1 = erfValue(x1, cen, sig)

plt.plot(x1, y1, 'k.')

plt.text(x1, y1, "(%.2f, %.2f)"%(x1,y1))

x2 = cen+sig

y2 = erfValue(x2, cen, sig)

plt.plot(x2, y2, 'k.')

plt.text(x2, y2, "(%.2f, %.2f)"%(x2,y2))

x3 = cen-sig

y3 = erfValue(x3, cen, sig)

plt.plot(x3, y3, 'k.')

plt.text(x3, y3, "(%.2f, %.2f)"%(x3,y3))

plt.title("erf curve")

plt.show()

erfc = erfcValue(xx, cen, sig)

plt.figure()

plt.plot(xx,erfc,'b')

x1 = cen

y1 = erfcValue(x1, cen, sig)

plt.plot(x1, y1, 'k.')

plt.text(x1, y1, "(%.2f, %.2f)"%(x1,y1))

x2 = cen+sig

y2 = erfcValue(x2, cen, sig)

plt.plot(x2, y2, 'k.')

plt.text(x2, y2, "(%.2f, %.2f)"%(x2,y2))

x3 = cen-sig

y3 = erfcValue(x3, cen, sig)

plt.plot(x3, y3, 'k.')

plt.text(x3, y3, "(%.2f, %.2f)"%(x3,y3))

plt.title("erfc curve")

plt.show()

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