scipy.stats.truncnorm#

scipy.stats.truncnorm = <scipy.stats._continuous_distns.truncnorm_gen object>[source]#

A truncated normal continuous random variable.

As an instance of the rv_continuous class, truncnorm object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods

rvs(a, b, loc=0, scale=1, size=1, random_state=None)

Random variates.

pdf(x, a, b, loc=0, scale=1)

Probability density function.

logpdf(x, a, b, loc=0, scale=1)

Log of the probability density function.

cdf(x, a, b, loc=0, scale=1)

Cumulative distribution function.

logcdf(x, a, b, loc=0, scale=1)

Log of the cumulative distribution function.

sf(x, a, b, loc=0, scale=1)

Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).

logsf(x, a, b, loc=0, scale=1)

Log of the survival function.

ppf(q, a, b, loc=0, scale=1)

Percent point function (inverse of cdf — percentiles).

isf(q, a, b, loc=0, scale=1)

Inverse survival function (inverse of sf).

moment(order, a, b, loc=0, scale=1)

Non-central moment of the specified order.

stats(a, b, loc=0, scale=1, moments=’mv’)

Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).

entropy(a, b, loc=0, scale=1)

(Differential) entropy of the RV.

fit(data)

Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.

expect(func, args=(a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)

Expected value of a function (of one argument) with respect to the distribution.

median(a, b, loc=0, scale=1)

Median of the distribution.

mean(a, b, loc=0, scale=1)

Mean of the distribution.

var(a, b, loc=0, scale=1)

Variance of the distribution.

std(a, b, loc=0, scale=1)

Standard deviation of the distribution.

interval(confidence, a, b, loc=0, scale=1)

Confidence interval with equal areas around the median.

Notes

This distribution is the normal distribution centered on loc (default 0), with standard deviation scale (default 1), and truncated at a and b standard deviations from loc. For arbitrary loc and scale, a and b are not the abscissae at which the shifted and scaled distribution is truncated.

Note

If a_trunc and b_trunc are the abscissae at which we wish to truncate the distribution (as opposed to the number of standard deviations from loc), then we can calculate the distribution parameters a and b as follows:

a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale

This is a common point of confusion. For additional clarification, please see the example below.

Examples

>>> import numpy as np
>>> from scipy.stats import truncnorm
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

>>> a, b = 0.1, 2
>>> mean, var, skew, kurt = truncnorm.stats(a, b, moments='mvsk')

Display the probability density function (pdf):

>>> x = np.linspace(truncnorm.ppf(0.01, a, b),
...                 truncnorm.ppf(0.99, a, b), 100)
>>> ax.plot(x, truncnorm.pdf(x, a, b),
...        'r-', lw=5, alpha=0.6, label='truncnorm pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pdf:

>>> rv = truncnorm(a, b)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

>>> vals = truncnorm.ppf([0.001, 0.5, 0.999], a, b)
>>> np.allclose([0.001, 0.5, 0.999], truncnorm.cdf(vals, a, b))
True

Generate random numbers:

>>> r = truncnorm.rvs(a, b, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
../../_images/scipy-stats-truncnorm-1_00_00.png

In the examples above, loc=0 and scale=1, so the plot is truncated at a on the left and b on the right. However, suppose we were to produce the same histogram with loc = 1 and scale=0.5.

>>> loc, scale = 1, 0.5
>>> rv = truncnorm(a, b, loc=loc, scale=scale)
>>> x = np.linspace(truncnorm.ppf(0.01, a, b),
...                 truncnorm.ppf(0.99, a, b), 100)
>>> r = rv.rvs(size=1000)
>>> fig, ax = plt.subplots(1, 1)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim(a, b)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
../../_images/scipy-stats-truncnorm-1_01_00.png

Note that the distribution is no longer appears to be truncated at abscissae a and b. That is because the standard normal distribution is first truncated at a and b, then the resulting distribution is scaled by scale and shifted by loc. If we instead want the shifted and scaled distribution to be truncated at a and b, we need to transform these values before passing them as the distribution parameters.

>>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale
>>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale)
>>> x = np.linspace(truncnorm.ppf(0.01, a, b),
...                 truncnorm.ppf(0.99, a, b), 100)
>>> r = rv.rvs(size=10000)
>>> fig, ax = plt.subplots(1, 1)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim(a-0.1, b+0.1)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
../../_images/scipy-stats-truncnorm-1_02_00.png