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Module « scipy.special »

Fonction stdtrit - module scipy.special

Signature de la fonction stdtrit

def stdtrit(*args, **kwargs) 

Description

help(scipy.special.stdtrit)

stdtrit(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

stdtrit(df, p, out=None)

The `p`-th quantile of the student t distribution.

This function is the inverse of the student t distribution cumulative
distribution function (CDF), returning `t` such that `stdtr(df, t) = p`.

Returns the argument `t` such that stdtr(df, t) is equal to `p`.

Parameters
----------
df : array_like
    Degrees of freedom
p : array_like
    Probability
out : ndarray, optional
    Optional output array for the function results

Returns
-------
t : scalar or ndarray
    Value of `t` such that ``stdtr(df, t) == p``

See Also
--------
stdtr : Student t CDF
stdtridf : inverse of stdtr with respect to `df`
scipy.stats.t : Student t distribution

Notes
-----
The student t distribution is also available as `scipy.stats.t`. Calling
`stdtrit` directly can improve performance compared to the ``ppf``
method of `scipy.stats.t` (see last example below).

Examples
--------
`stdtrit` represents the inverse of the student t distribution CDF which
is available as `stdtr`. Here, we calculate the CDF for ``df`` at
``x=1``. `stdtrit` then returns ``1`` up to floating point errors
given the same value for `df` and the computed CDF value.

>>> import numpy as np
>>> from scipy.special import stdtr, stdtrit
>>> import matplotlib.pyplot as plt
>>> df = 3
>>> x = 1
>>> cdf_value = stdtr(df, x)
>>> stdtrit(df, cdf_value)
0.9999999994418539

Plot the function for three different degrees of freedom.

>>> x = np.linspace(0, 1, 1000)
>>> parameters = [(1, "solid"), (2, "dashed"), (5, "dotted")]
>>> fig, ax = plt.subplots()
>>> for (df, linestyle) in parameters:
...     ax.plot(x, stdtrit(df, x), ls=linestyle, label=f"$df={df}$")
>>> ax.legend()
>>> ax.set_ylim(-10, 10)
>>> ax.set_title("Student t distribution quantile function")
>>> plt.show()

The function can be computed for several degrees of freedom at the same
time by providing a NumPy array or list for `df`:

>>> stdtrit([1, 2, 3], 0.7)
array([0.72654253, 0.6172134 , 0.58438973])

It is possible to calculate the function at several points for several
different degrees of freedom simultaneously by providing arrays for `df`
and `p` with shapes compatible for broadcasting. Compute `stdtrit` at
4 points for 3 degrees of freedom resulting in an array of shape 3x4.

>>> dfs = np.array([[1], [2], [3]])
>>> p = np.array([0.2, 0.4, 0.7, 0.8])
>>> dfs.shape, p.shape
((3, 1), (4,))

>>> stdtrit(dfs, p)
array([[-1.37638192, -0.3249197 ,  0.72654253,  1.37638192],
       [-1.06066017, -0.28867513,  0.6172134 ,  1.06066017],
       [-0.97847231, -0.27667066,  0.58438973,  0.97847231]])

The t distribution is also available as `scipy.stats.t`. Calling `stdtrit`
directly can be much faster than calling the ``ppf`` method of
`scipy.stats.t`. To get the same results, one must use the following
parametrization: ``scipy.stats.t(df).ppf(x) = stdtrit(df, x)``.

>>> from scipy.stats import t
>>> df, x = 3, 0.5
>>> stdtrit_result = stdtrit(df, x)  # this can be faster than below
>>> stats_result = t(df).ppf(x)
>>> stats_result == stdtrit_result  # test that results are equal
True

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