scipy.stats.Uniform.

ccdf#

Uniform.ccdf(x, y=None, /, *, method=None)[source]#

Complementary cumulative distribution function

The complementary cumulative distribution function (“CCDF”), denoted $G(x)$ , is the complement of the cumulative distribution function $F(x)$ ; i.e., probability the random variable $X$ will assume a value greater than $x$ :

$G(x) = 1 - F(x) = P(X > x)$

A two-argument variant of this function is:

$G(x, y) = 1 - F(x, y) = P(X < x \text{ or } X > y)$

ccdf accepts x for $x$ and y for $y$ .

Parameters:

x, yarray_like

The arguments of the CCDF. x is required; y is optional.

method{None, ‘formula’, ‘logexp’, ‘complement’, ‘quadrature’, ‘addition’}

The strategy used to evaluate the CCDF. By default (None), the infrastructure chooses between the following options, listed in order of precedence.

'formula': use a formula for the CCDF itself
'logexp': evaluate the log-CCDF and exponentiate
'complement': evaluate the CDF and take the complement
'quadrature': numerically integrate the PDF

The two-argument form chooses between:

'formula': use a formula for the CCDF itself
'addition': compute the CDF at x and the CCDF at y, then add

Not all method options are available for all distributions. If the selected method is not available, a NotImplementedError will be raised.

Returns:

outarray: The CCDF evaluated at the provided argument(s).

See also

cdf
logccdf

Notes

Suppose a continuous probability distribution has support $[l, r]$ . The CCDF $G(x)$ is related to the probability density function $f(x)$ by:

$G(x) = \int_x^r f(u) du$

The two argument version is:

$G(x, y) = \int_l^x f(u) du + \int_y^r f(u) du$

The CCDF returns its minimum value of $0$ for $x ≥ r$ and its maximum value of $1$ for $x ≤ l$ .

The CCDF is also known as the “survival function”.

References

[1]

Cumulative distribution function, Wikipedia, https://en.wikipedia.org/wiki/Cumulative_distribution_function#Derived_functions

Examples

Instantiate a distribution with the desired parameters:

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

Evaluate the CCDF at the desired argument:

>>> X.ccdf(0.25)
0.25
>>> np.allclose(X.ccdf(0.25), 1-X.cdf(0.25))
True

Evaluate the complement of the cumulative probability between two arguments:

>>> X.ccdf(-0.25, 0.25) == X.cdf(-0.25) + X.ccdf(0.25)
True