scipy.special.nctdtr#

scipy.special.nctdtr(df, nc, t, out=None) = <wrapped_ufunc 'nctdtr'>#

Cumulative distribution function of the non-central t distribution.

Parameters:

dfarray_like: Degrees of freedom of the distribution. Should be in range (0, inf).
ncarray_like: Noncentrality parameter.
tarray_like: Quantiles, i.e., the upper limit of integration.
outndarray, optional: Optional output array for the function results

Returns:

cdfscalar or ndarray: The calculated CDF. If all inputs are scalar, the return will be a float. Otherwise, it will be an array.

See also

nctdtrit: Inverse CDF (iCDF) 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 CDF of the non-central t distribution using the Boost Math C++ library [1].

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

Array API Standard Support

nctdtr 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. nctdtr 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

>>> import numpy as np
>>> from scipy import special
>>> from scipy import stats
>>> import matplotlib.pyplot as plt

Plot the CDF of the non-central t distribution, for nc=0. Compare with the t-distribution from scipy.stats:

>>> x = np.linspace(-5, 5, num=500)
>>> df = 3
>>> nct_stats = stats.t.cdf(x, df)
>>> nct_special = special.nctdtr(df, 0, x)

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> ax.plot(x, nct_stats, 'b-', lw=3)
>>> ax.plot(x, nct_special, 'r-')
>>> plt.show()

../../_images/scipy-special-nctdtr-1.png