scipy.special.nctdtr#

scipy.special.nctdtr(df, nc, t, out=None) = <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.

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