I stumbled upon some peculiar behavior of random numbers in Python , specifically I use the module numpy.random.
Consider the following expression:
n = 50
N = 1000
np.histogram(np.sum(np.random.randint(0, 2, size=(n, N)), axis=0), bins=n+1)[0]
In the limit of large N
I would expect a binomial distribution (for the interested reader, this simulates the Ehrenfest model) and for large n
a normal distribution. A typical output however, looks like this:
array([
1, 0, 0, 1, 0, 2, 0, 1, 0, 15, 0,
12, 0, 18, 0, 39, 0, 64, 0, 62, 0, 109,
0, 97, 0, 107, 0, 114, 0, 102, 0, 92, 0,
55, 0, 46, 0, 35, 0, 10, 0, 9, 0, 4,
0, 0, 0, 3, 0, 1, 1
])
With the statement from above, I can't explain the occurrence of the zeros in the histogram - am I missing something obvious here?
You're using histogram
wrong. The bins aren't where you think they are. They don't go from 0 to 50; they go from the minimum input value to the maximum input value. The 0s represent bins that lie entirely between two integers.
Try it with numpy.bincount
:
In [31]: n = 50
In [32]: N = 5000
In [33]: np.bincount(np.sum(np.random.randint(0, 2, size=(n, N)), axis=0))
Out[33]:
array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 7, 13, 22, 46, 75, 126, 220, 305, 367, 461, 550, 578,
517, 471, 438, 314, 189, 146, 76, 50, 17, 9, 2, 1])
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