scipy.stats.Normal.

support#

Normal.support()[source]#

Support of the random variable

The support of a random variable is set of all possible outcomes; i.e., the subset of the domain of argument \(x\) for which the probability density function \(f(x)\) is nonzero.

This function returns lower and upper bounds of the support.

Returns:

outtuple of Array: The lower and upper bounds of the support.

See also

pdf

Notes

Suppose a continuous probability distribution has support (l, r). The following table summarizes the value returned by methods of ContinuousDistribution for arguments 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 the cdf and related methods, 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 of ContinuousDistribution for arguments at the boundaries of the domain 0 to 1.

Method	`x = 0`	`x = 1`
`icdf(x)`	`l`	`r`
`icdf(x)`	`r`	`l`

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

References

[1]

Support (mathematics), Wikipedia, https://en.wikipedia.org/wiki/Support_(mathematics)

Examples

Instantiate a distribution with the desired parameters:

>>> from scipy import stats
>>> X = stats.Uniform(a=-0.5, b=0.5)

Retrieve the support of the distribution:

>>> X.support()
(-0.5, 0.5)

For a distribution with infinite support,

>>> X = stats.Normal()
>>> X.support()
(-inf, inf)

Due to underflow, the numerical value returned by the PDF may be zero even for arguments within the support, even if the true value is nonzero. In such cases, the log-PDF may be useful.

>>> X.pdf([-100., 100.])
array([0., 0.])
>>> X.logpdf([-100., 100.])
array([-5000.91893853, -5000.91893853])

Use cases for the log-CDF and related methods are analogous.