`scipy.stats._distribution_infrastructure:truncate`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_distribution_infrastructure.py:4588

Signature

def truncate(X, lb = -inf, ub = inf)

Summary

Truncate the support of a random variable.

Extended Summary

Given a random variable X, truncate returns a random variable with support truncated to the interval between lb and ub. The underlying probability density function is normalized accordingly.

Parameters

X : `ContinuousDistribution`: The random variable to be truncated.
lb, ub : float array-like: The lower and upper truncation points, respectively. Must be broadcastable with one another and the shape of X.

Returns

X : `ContinuousDistribution`: The truncated random variable.

Examples

Compare against `scipy.stats.truncnorm`, which truncates a standard normal, *then* shifts and scales it.

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
loc, scale, lb, ub = 1, 2, -2, 2
X = stats.truncnorm(lb, ub, loc, scale)
Y = scale * stats.truncate(stats.Normal(), lb, ub) + loc
x = np.linspace(-3, 5, 300)

✓

plt.plot(x, X.pdf(x), '-', label='X')
plt.plot(x, Y.pdf(x), '--', label='Y')
plt.xlabel('x')
plt.ylabel('PDF')
plt.title('Truncated, then Shifted/Scaled Normal')
plt.legend()

✗

<matplotlib.legend.Legend object at 0x7f3f68548440>

plt.show()

✓

However, suppose we wish to shift and scale a normal random variable, then truncate its support to given values. This is straightforward with `truncate`.

Z = stats.truncate(scale * stats.Normal() + loc, lb, ub)

✓

Z.plot()

✗

<Axes: title={'center': 'truncate(2.0*StandardNormal() + 1.0, lb=-2.0, ub=2.0)'}, xlabel='$x$', ylabel='$pdf$'>

plt.show()

✓

Furthermore, `truncate` can be applied to any random variable:

Rayleigh = stats.make_distribution(stats.rayleigh)
W = stats.truncate(Rayleigh(), lb=0.5, ub=3)

✓

W.plot()

✗

<Axes: title={'center': 'truncate(Rayleigh(), lb=0.5, ub=3.0)'}, xlabel='$x$', ylabel='$pdf$'>

plt.show()

✓