scipy.stats._probability_distribution:_ProbabilityDistribution.support

Notes

Suppose a continuous probability distribution has support (l, r). The following table summarizes the value returned by several methods when the argument is outside the support.

+----------------+---------------------+---------------------+
| Method         | Value for ``x < l`` | Value for ``x > r`` |
+================+=====================+=====================+
| ``pdf(x)``     | 0                   | 0                   |
+----------------+---------------------+---------------------+
| ``logpdf(x)``  | -inf                | -inf                |
+----------------+---------------------+---------------------+
| ``cdf(x)``     | 0                   | 1                   |
+----------------+---------------------+---------------------+
| ``logcdf(x)``  | -inf                | 0                   |
+----------------+---------------------+---------------------+
| ``ccdf(x)``    | 1                   | 0                   |
+----------------+---------------------+---------------------+
| ``logccdf(x)`` | 0                   | -inf                |
+----------------+---------------------+---------------------+

For discrete distributions, the same table is applicable with pmf and logpmf substituted for pdf and logpdf.

For the cdf and related methods of continuous distributions, the inequality need not be strict; i.e. the tabulated value is returned when the method is evaluated at the corresponding boundary.

The following table summarizes the value returned by the inverse methods for arguments 0 and 1, whether the distribution is continuous or discrete.

+-------------+-----------+-----------+
| Method      | ``x = 0`` | ``x = 1`` |
+=============+===========+===========+
| ``icdf(x)`` | ``l``     | ``r``     |
+-------------+-----------+-----------+
| ``icdf(x)`` | ``r``     | ``l``     |
+-------------+-----------+-----------+

For the inverse log-functions, the same values are returned for x = log(0) and x = log(1). All inverse functions return nan when evaluated at an argument outside the domain 0 to 1.