scipy.stats.Mixture.

iccdf#

Mixture.iccdf(p, /, *, method=None)[source]#

Inverse complementary cumulative distribution function.

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

$G^{-1}(p) = x \quad \text{s.t.} \quad G(x) = p$

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 $\chi$ for which $G(x)$ is no greater than $p$ .

G^{- 1} (p) = min_{χ} s.t. G (x) \leq p

$G^{-1}(p) = \min_\chi \quad \text{s.t.} \quad G(x) ≤ p$

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

Parameters:

parray_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:

outarray: The inverse CCDF evaluated at the provided argument.

See also

icdf
ilogccdf

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

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

>>> X.iccdf([-0.1, 0, 1, 1.1])
array([ nan,  0.5, -0.5,  nan])