Epps Singleton 2samp

---
name: epps-singleton-2samp
description: Compute the epps_singleton_2samp metric — provided by scipy.stats. Use when the user has predictions and ground-truth and needs to compute epps_singleton_2samp, or asks how to score with epps_singleton_2samp.
metadata:
  skill_kind: metric
  source_lib: scipy.stats
  import_path: scipy.stats.epps_singleton_2samp
  source: library_introspection
---

# epps-singleton-2samp

> Metric `epps_singleton_2samp` from `scipy.stats` (scipy.stats.epps_singleton_2samp)

## When to invoke this skill

The user has predictions + ground truth and asks to evaluate with epps_singleton_2samp, or
mentions `scipy.stats.epps_singleton_2samp` directly, or wants the standard scipy.stats implementation.

## Reference signature

```python
from scipy.stats import epps_singleton_2samp

# epps_singleton_2samp(x, y, t=(0.4, 0.8), *, axis=0, nan_policy='propagate', keepdims=False)
```

## Library docstring

```
Compute the Epps-Singleton (ES) test statistic.

Test the null hypothesis that two samples have the same underlying
probability distribution.

Parameters
----------
x, y : array-like
    The two samples of observations to be tested. Input must not have more
    than one dimension. Samples can have different lengths, but both
    must have at least five observations.
t : array-like, optional
    The points (t1, ..., tn) where the empirical characteristic function is
    to be evaluated. It should be positive distinct numbers. The default
    value (0.4, 0.8) is proposed in [1]_. Input must not have more than
    one dimension.
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.

    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
statistic : float
    The test statistic.
pvalue : float
    The associated p-value based on the asymptotic chi2-distribution.

See Also
--------

:func:`ks_2samp`, :func:`anderson_ksamp`
    ..


Notes
-----
Testing whether two samples are generated by the same underlying
distribution is a classical question in statistics. A widely used test is
the Kolmogorov-Smirnov (KS) test which relies on the empirical
distribution function. Epps and Singleton introduce a test b
```

## Quick recipe

```python
import scipy.stats as _m
score = _m.epps_singleton_2samp(y_true, y_pred)
```

## Don'ts

- Don't reimplement when the library version handles edge cases (NaN, ties, empty inputs) better than a hand-rolled formula.
- Always check the library version's argument order — sklearn is `(y_true, y_pred)` while torchmetrics is `(preds, target)`.