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. Should be in range (-1e6, 1e6).

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.

Examples

>>> 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()