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Uniform Fences Don't Give Uniform Data

From: andrew cooke <andrew@...>

Date: Thu, 29 Mar 2012 10:10:39 -0300

from random import random
from itertools import chain
from collections import Counter

def split(k):
    fences = list(sorted(chain([0], [random() for i in range(k-1)], [1])))
    return [j - i for i,j in zip(fences, fences[1:])]

def bin(n, data):
    return Counter(int(x * n) for x in chain(*data))

def plot(bins, n, w):
    m = max(bins.values())
    for b in sorted(bins):
        print '%4.2f %s' % (b / float(n), '*' * int(bins[b] * w / m))

k = 4
n = 50
print split(k)
b = bin(n, (split(k) for i in range(n*1000/k)))
print b
plot(b, n, 70)


0.00 **********************************************************************
0.02 ******************************************************************
0.04 ******************************************************************
0.06 ***********************************************************
0.08 ************************************************************
0.10 ********************************************************
0.12 ****************************************************
0.14 *************************************************
0.16 ************************************************
0.18 *********************************************
0.20 ********************************************
0.22 *******************************************
0.24 **************************************
0.26 **************************************
0.28 **********************************
0.30 *********************************
0.32 ******************************
0.34 *****************************
0.36 ***************************
0.38 ***************************
0.40 *************************
0.42 *********************
0.44 *********************
0.46 *******************
0.48 *****************
0.50 *****************
0.52 ***************
0.54 **************
0.56 *************
0.58 ***********
0.60 **********
0.62 *********
0.64 ********
0.66 ********
0.68 *******
0.70 ******
0.72 *****
0.74 ****
0.76 ***
0.78 ***
0.80 **
0.82 **
0.84 *
0.86 
0.88 
0.90 
0.92 
0.94 
0.96 

Andrew

N-1 Dimensional Planes

From: andrew cooke <andrew@...>

Date: Thu, 29 Mar 2012 11:32:13 -0300

Hmmm.  So the post above came from misunderstanding what someone meant by
"uniform".

"Choose N numbers, X[i], that sum to S (sum(X) = S), that are uniformly
distributed" - which doesn't mean that each is indiviudally uniform, but that
the X[i], when repeatedly selected, uniformly fill an N-1 dimensional plane.

(It's not clear to me that fences do that either, but the plot above doesn't
disprove it)

Andrew

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