How to get a normal distribution within a range in numpy?

Question

In machine learning task. We should get a group of random w.r.t normal distribution with bound. We can get a normal distribution number with np.random.normal() but it does't offer any bound parameter. I want to know how to do that?

Answer 1

The parametrization of truncnorm is complicated, so here is a function that translates the parametrization to something more intuitive:

from scipy.stats import truncnorm

def get_truncated_normal(mean=0, sd=1, low=0, upp=10):
    return truncnorm(
        (low - mean) / sd, (upp - mean) / sd, loc=mean, scale=sd)

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How to use it?

1. Instance the generator with the parameters: mean, standard deviation, and truncation range:

   >>> X = get_truncated_normal(mean=8, sd=2, low=1, upp=10)
   

2. Then, you can use X to generate a value:

   >>> X.rvs()
   6.0491227353928894
   

3. Or, a numpy array with N generated values:

   >>> X.rvs(10)
   array([ 7.70231607,  6.7005871 ,  7.15203887,  6.06768994,  7.25153472,
           5.41384242,  7.75200702,  5.5725888 ,  7.38512757,  7.47567455])
   

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A Visual Example

Here is the plot of three different truncated normal distributions:

X1 = get_truncated_normal(mean=2, sd=1, low=1, upp=10)
X2 = get_truncated_normal(mean=5.5, sd=1, low=1, upp=10)
X3 = get_truncated_normal(mean=8, sd=1, low=1, upp=10)

import matplotlib.pyplot as plt
fig, ax = plt.subplots(3, sharex=True)
ax[0].hist(X1.rvs(10000), normed=True)
ax[1].hist(X2.rvs(10000), normed=True)
ax[2].hist(X3.rvs(10000), normed=True)
plt.show()