"""

Approximate Cumulative Distribution Function

--------------------------------------------

Calculates the cumulative distribution function (CDF)

of the normal distribution based on an approximation by George Marsaglia:

Marsaglia, George (2004). "Evaluating the Normal Distribution".

Journal of Statistical Software 11 (4).

16 digit precision for 300 iterations when x = 10.

Equation:

f(x) = 1/2 + pdf(x) * (x + (x^3/3) + (x^5/3*5) + (x^7/3*7) + ...)

"""

from algorithms.math import std_normal_pdf

def cdf(x, iterations=300):

"""

Calculates the cumulative distribution function of the normal distribution.

Uses a taylor exponent to calculate this.

:param x: An integer that represents the taylor exponent.

:param iterations: An integer representing the number of iterations.

:rtype: The normal distribution

"""

product = 1.0

taylor_exp = [x]

for i in range(3, iterations, 2):

product *= i

taylor_exp.append(float(x**i)/product)

taylor_fact = sum(taylor_exp)

return (0.5 + (taylor_fact * std_normal_pdf.pdf(x, mean=0, std_dev=1)))