scipy.special.nctdtr — SciPy v1.15.2 Manual (original) (raw)

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

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()