scipy.special.nctdtrit#

scipy.special.nctdtrit(df, nc, p, out=None) = <wrapped_ufunc 'nctdtrit'>#

Inverse cumulative distribution function of the non-central t distribution.

See nctdtr for more details.

Parameters:

dfarray_like: Degrees of freedom of the distribution. Should be in range (0, inf).
ncarray_like: Noncentrality parameter.
parray_like: CDF values, in range (0, 1].
outndarray, optional: Optional output array for the function results

Returns:

tscalar or ndarray: Quantiles

See also

nctdtr: CDF of the non-central t distribution.
nctdtridf: Calculate degrees of freedom, given CDF and iCDF values.
nctdtrinc: Calculate non-centrality parameter, given CDF iCDF values.

Notes

This function calculates the quantile of the non-central t distribution using the Boost Math C++ library [1].

Note that the argument order of nctdtrit is different from that of the similar ppf method of scipy.stats.nct: t is the last parameter of nctdtrit but the first parameter of scipy.stats.nct.ppf.

Array API Standard Support

nctdtrit 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. nctdtrit does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

>>> from scipy.special import nctdtr, nctdtrit

Compute the CDF for several values of t:

>>> t = [0.5, 1, 1.5]
>>> p = nctdtr(3, 1, t)
>>> p
array([0.29811049, 0.46922687, 0.6257559 ])

Compute the inverse. We recover the values of t, as expected:

>>> nctdtrit(3, 1, p)
array([0.5, 1. , 1.5])