`scipy.stats._probability_distribution:_ProbabilityDistribution.icdf`

source: /scipy/stats/_probability_distribution.py :1134

Signature

def icdf ( self , p , / , method )

Summary

Inverse of the cumulative distribution function.

Extended Summary

For monotonic continuous distributions, the inverse of the cumulative distribution function ("inverse CDF"), denoted $F^{- 1} (p)$ , is the argument $x$ for which the cumulative distribution function $F (x)$ evaluates to $p$ .

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

When a strict "inverse" of the cumulative distribution function does not exist (e.g. discrete random variables), the "inverse CDF" is defined by convention as the smallest value within the support $χ$ for which $F (x)$ is at least $p$ .

F^{- 1} (p) = χ min s.t. F (x) \geq p

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

Parameters

p : array_like

The argument of the inverse CDF.

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

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

'formula': use a formula for the inverse CDF itself
'complement': evaluate the inverse CCDF at the complement of p
'inversion': solve numerically for the argument at which the CDF 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 CDF evaluated at the provided argument.

Notes

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

The inverse CDF is also known as the quantile function, percentile function, and percent-point 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 inverse CDF at the desired argument:

X.icdf(0.25)

✗

np.allclose(X.cdf(X.icdf(0.25)), 0.25)

✓

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

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

✓

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.icdf