`scipy.stats._distribution_infrastructure:truncate`

source: /scipy/stats/_distribution_infrastructure.py :4589

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.

Notes

Array API Standard Support

truncate has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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()

✗

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()

✗

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()

✗

plt.show()

✓