scipy.stats._continuous_distns:truncnorm_gen

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.

%(example)s

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()

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()