`scipy.stats._probability_distribution:_ProbabilityDistribution.iccdf`

source: /scipy/stats/_probability_distribution.py :1342

Signature

def iccdf ( self , p , / , method )

Summary

Inverse complementary cumulative distribution function.

Extended Summary

The inverse complementary cumulative distribution function ("inverse CCDF"), denoted $G^{- 1} (p)$ , is the argument $x$ for which the complementary cumulative distribution function $G (x)$ evaluates to $p$ .

G^{- 1} (p) = x s.t. G (x) = p

When a strict "inverse" of the complementary cumulative distribution function does not exist (e.g. discrete random variables), the "inverse CCDF" is defined by convention as the smallest value within the support $χ$ for which $G (x)$ is no greater than $p$ .

G^{- 1} (p) = χ min s.t. G (x) \leq p

iccdf accepts p for $p \in [0, 1]$ .

Parameters

p : array_like

The argument of the inverse CCDF.

method : {None, 'formula', 'complement', 'inversion'}

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

'formula': use a formula for the inverse CCDF itself
'complement': evaluate the inverse CDF at the complement of p
'inversion': solve numerically for the argument at which the CCDF is equal to p

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 inverse CCDF evaluated at the provided argument.

Notes

Suppose a probability distribution has support $[l, r]$ . The inverse CCDF returns its minimum value of $l$ at $p = 1$ and its maximum value of $r$ at $p = 0$ . Because the CCDF has range $[0, 1]$ , the inverse CCDF is only defined on the domain $[0, 1]$ ; for $p < 0$ and $p > 1$ , iccdf returns nan.

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 inverse CCDF at the desired argument:

X.iccdf(0.25)

✗

np.allclose(X.iccdf(0.25), X.icdf(1-0.25))

✓

This function returns NaN when the argument is outside the domain.

X.iccdf([-0.1, 0, 1, 1.1])

✓

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.iccdf