I am looking for a function in Numpy or Scipy (or any rigorous Python library) that will give me the cumulative normal distribution function in Python.
Here's an example:
>>> from scipy.stats import norm
>>> norm.cdf(1.96)
0.9750021048517795
>>> norm.cdf(-1.96)
0.024997895148220435
In other words, approximately 95% of the standard normal interval lies within two standard deviations, centered on a standard mean of zero.
If you need the inverse CDF:
>>> norm.ppf(norm.cdf(1.96))
array(1.9599999999999991)