scipy.stats.Normal.

icdf#

Normal.icdf(p, /, *, method=None)[source]#

Inverse of the cumulative distribution function.

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 \(p\).

\[F^{-1}(p) = x \quad \text{s.t.} \quad F(x) = p\]

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

Parameters:

parray_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:

outarray: The inverse CDF evaluated at the provided argument.

See also

cdf
ilogcdf

Notes

Suppose a continuous 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.

References

[1]

Quantile function, Wikipedia, https://en.wikipedia.org/wiki/Quantile_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)
-0.25
>>> np.allclose(X.cdf(X.icdf(0.25)), 0.25)
True

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

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