# 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

```>>> 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()
```