`scipy.stats._probability_distribution:_ProbabilityDistribution.ccdf`

source: /scipy/stats/_probability_distribution.py :1227

Signature

def ccdf ( self , x , y , / , method )

Summary

Complementary cumulative distribution function

Extended Summary

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 or X > y)

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

Parameters

x, y : array_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 (or, in the discrete case, sum the PMF)

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

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

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) d u

The two argument version is:

G (x, y) = \int_{l}^{x} f (u) d u + \int_{y}^{r} f (u) d u

The CCDF returns its minimum value of $0$ for $x \geq r$ and its maximum value of $1$ for $x \leq l$ .

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

G (x) = u = ⌊ x + 1 ⌋ \sum r f (u)

The CCDF evaluates to its minimum value of $0$ for $x \geq r$ and its maximum value of $1$ for $x < l$ .

The CCDF is also known as the "survival function".

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)

✗

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

✓

Evaluate the complement of the cumulative probability between two arguments:

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

✗

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.ccdf