scipy.stats.

truncate

scipy.stats.truncate(X, lb=-inf, ub=inf)

Truncate the support of a random variable.

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:

XContinuousDistribution

The random variable to be truncated.

lb, ubfloat array-like

The lower and upper truncation points, respectively. Must be broadcastable with one another and the shape of X.

Returns:

XContinuousDistribution

The truncated random variable.

References

[1]

“Truncated Distribution”. Wikipedia. https://en.wikipedia.org/wiki/Truncated_distribution

Examples

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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, ub=3)
>>> W.plot()
>>> plt.show()

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