scipy.special.smirnovi#

scipy.special.smirnovi(n, p, out=None) = <wrapped_ufunc 'smirnovi'>#

Inverse to smirnov.

Returns d such that smirnov(n, d) == p, the critical value corresponding to p.

Parameters:

nint: Number of samples
pfloat array_like: Probability
outndarray, optional: Optional output array for the function results

Returns:

scalar or ndarray: The value(s) of smirnovi(n, p), the critical values.

See also

smirnov: The Survival Function (SF) for the distribution
scipy.stats.ksone: Provides the functionality as a continuous distribution
kolmogorov, kolmogi: Functions for the two-sided distribution
scipy.stats.kstwobign: Two-sided Kolmogorov-Smirnov distribution, large n

Notes

For historical reasons this function is exposed in scipy.special, but the recommended way to achieve the most accurate CDF/SF/PDF/PPF/ISF computations is to use the scipy.stats.ksone distribution.

Array API Standard Support

smirnovi has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	✅	⛔
JAX	✅	⛔
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but typically none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. smirnovi does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

Examples

>>> from scipy.special import smirnovi, smirnov

>>> n = 24
>>> deviations = [0.1, 0.2, 0.3]

Use smirnov to compute the complementary CDF of the Smirnov distribution for the given number of samples and deviations.

>>> p = smirnov(n, deviations)
>>> p
array([0.58105083, 0.12826832, 0.01032231])

The inverse function smirnovi(n, p) returns deviations.

>>> smirnovi(n, p)
array([0.1, 0.2, 0.3])