Describe the issue:

For empty inputs (size=0), quantile yields an Index error:

>> np.quantile([], 0.5)
IndexError: index -1 is out of bounds for axis 0 with size 0

While median yields np.float64(nan) (with warnings):

>> np.median([])
np.float64(nan)

The See also section, suggests np.quantile(..., 0.5) == np.median(...), else I find no information on the case size=0, or any mention of raised errors.
The behavior of median is consistent with mean, which follows the specification of https://data-apis.org/array-api/latest/API_specification/generated/array_api.mean.html.

I would expect quantile to return NaN for empty arrays.

Reproduce the code example:

import numpy as np
np.quantil([], 0.5)

Error message:

Python and NumPy Versions:

2.2.6
3.12.6 | packaged by conda-forge | (main, Sep 30 2024, 18:08:52) [GCC 13.3.0]

Runtime Environment:

No response

Context for the issue:

No response