np.random.choice has a gap in histogram

Question

I am using np.random.choice to construct a histogram of the sum of throwing 2 evenly weighted dice. However, when I run the code, the values for 7, which should have the most returns, are missing.

import numpy as np
import matplotlib.pyplot as plt

values = [1, 2, 3, 4, 5, 6]
z = 1/6
x = np.random.choice(values, 1000000, p=[z, z, z, z, z, z])
y = np.random.choice(values, 1000000, p=[z, z, z, z, z, z])

plt.hist(x + y, 12, color="green", edgecolor='black', linewidth=1.2, label="Uniform Dist", rwidth=.75)
plt.show()

Any suggestions on what is going wrong?

Answer 1

There are no values inthe interval 6.167 <= x < 7.0 . The numbers 7 are included in the interval 7.0 <= x < 7.833 .

I'd recommend to plot a bar plot of the discrete frequencies.

plt.bar(*np.unique(x+y, return_counts=True))

Answer 2

The problem is that plt.hist binning algorithm is suitable for real values, not for integer (discrete) values.

Explanation

Let's see bins proposed by matplotlib:

n, bins, _ = plt.hist(x + y, bb, color="green", edgecolor='black', linewidth=1.2, label="Uniform Dist", rwidth=.75)

The bins is:

array([ 2.        ,  2.83333333,  3.66666667,  4.5       ,  5.33333333,
        6.16666667,  7.        ,  7.83333333,  8.66666667,  9.5       ,
       10.33333333, 11.16666667, 12.        ])

Sixth bar has range [bins[5], bins[6]) equal to [6.17, 7.00) - notice, that it is half-open. Therefore no integer belongs to this range.

Solution

The solution is to manually set bins:

values = x + y
bins = np.arange(np.min(values) - .5, np.max(values) + 0.5, 1)

plt.hist(values, bins, color="green", edgecolor='black', linewidth=1.2, label="Uniform Dist", rwidth=.75)

bins is equal to array([0.5, 1.5, 2.5, 3.5, 4.5, 5.5, ..., 10.5, 11.5, 12.5]) .