Gaussian discretization

README.md

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gbin.py

"""
Divides a numeric range into n breaks based
on equal areas under a gaussian curve.

Raw numerics are converted to their 'z' score 
(normalized to mean=0, sd=1) and then their 
position is looked up inside an equal area
division of the region under a bell curve.

tim@menzies.us,  (c) 2012
Creative Commons Attribution 3.0 (Unported) [1]

Share and Enjoy! [2]
;-)

{ 1: "http://goo.gl/o9gzT"; 2:"http://goo.gl/7l4YL"}
"""

def gbin(n,bins,mean,sd) :
    "Main driver: convert 'n' into one of x 'bins'."
    return bin((n - mean) / sd, breaks[bins])

breaks = {
  2:                         [0],
  3:                  [-0.43,    0.43],
  4:                  [-0.67, 0, 0.67],
  5:            [-0.84,-0.25, 0, 0.25, 0.84],
  6:            [-0.97,-0.43, 0, 0.43, 0.97],
  7:      [-1.07,-0.57,-0.18, 0, 0.18, 0.57, 1.07],
  8:      [-1.15,-0.67,-0.32, 0, 0.32, 0.67, 1.15],
  9:[-1.22,-0.76,-0.43,-0.14,    0.14, 0.43, 0.76, 1.22],
 10:[-1.28,-0.84,-0.52,-0.25, 0, 0.25, 0.52, 0.84, 1.28]
}

def bin(val,breaks, ninf = -10*10) :
    "Low-level discretization of 'val' using the supplied 'breaks'."
    before = ninf
    last   = 0
    for i,now in enumerate(breaks) :
        if val > before and val <= now:
            return i
        before = now
        last = i
    return last+1