How to generate a random normal distribution of integers

One other way to get a discrete distribution that looks like the normal distribution is to draw from a multinomial distribution where the probabilities are calculated from a normal distribution.

import scipy.stats as ss
import numpy as np
import matplotlib.pyplot as plt

x = np.arange(-10, 11)
xU, xL = x + 0.5, x - 0.5 
prob = ss.norm.cdf(xU, scale = 3) - ss.norm.cdf(xL, scale = 3)
prob = prob / prob.sum() # normalize the probabilities so their sum is 1
nums = np.random.choice(x, size = 10000, p = prob)
plt.hist(nums, bins = len(x))

Here, np.random.choice picks an integer from [-10, 10]. The probability for selecting an element, say 0, is calculated by p(-0.5 < x < 0.5) where x is a normal random variable with mean zero and standard deviation 3. I chose a std. dev. of 3 because this way p(-10 < x < 10) is almost 1.

The result looks like this:

enter image description here

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