Inf values scipy.stats.truncnorm

Question

I am using this code to sample from a truncated normal:

np.random.seed(1234)
Z = truncnorm.rvs(a = 31.399904/0.822358, b = np.inf, loc = 31.399904, scale = 0.822358)

It generates inf values for Z, which mess up with the rest of my code. Would you have an idea how to avoid this?

Answer 1

If you want a truncnorm supported on [lower, upper] use

X = stats.truncnorm(
    (lower - mu) / sigma, (upper - mu) / sigma, loc=mu, scale=sigma)

For example, if you want a truncated norm supported on [31.399904, np.inf] with mean 32 and std deviation 0.822358, then you would use

import scipy.stats as stats
import matplotlib.pyplot as plt

lower, upper = 31.399904, np.inf
mu, sigma = 32, 0.822358
X = stats.truncnorm(
    (lower - mu) / sigma, (upper - mu) / sigma, loc=mu, scale=sigma)
N = stats.norm(loc=mu, scale=sigma)
data = X.rvs(10000)

fig, ax = plt.subplots(2, sharex=True)
ax[0].hist(data, density=True)
ax[1].hist(N.rvs(10000), density=True)
plt.show()

The top histogram shows the distribution of a sample from the truncnorm, the lower histogram show the distribution of a sample from a standard normal with the same mean and std deviation.

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If you also want the mean mu to equal the left endpoint of the support, then you would use

lower, upper = 31.399904, np.inf
mu, sigma = lower, 0.822358
Z = stats.truncnorm.rvs((lower - mu) / sigma, (upper - mu) / sigma, loc=mu, scale=sigma)

which is equivalent to

Z = stats.truncnorm.rvs(0, np.inf, loc=31.399904, scale=0.822358)

For example,

In [47]: np.random.seed(1234)
In [49]: stats.truncnorm.rvs(0, np.inf, loc=31.399904, scale=0.822358)
Out[49]: 31.599232630594255

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The problem with

Z = truncnorm.rvs(a = 31.399904/0.822358, b = np.inf, loc = 31.399904, scale = 0.822358)

is that the mean is at loc=31.3999904, but the left endpoint is around 38.2:

In [51]: a = 31.399904/0.822358; a
Out[51]: 38.18276711602489

The most likely value of a truncnorm should be at its mean, but the mean falls outside of the support, [38.2, np.inf] . This contradiction leads to the bizarre behavior.