Power Divergence

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

# power-divergence

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

## When to invoke this skill

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

## Reference signature

```python
from scipy.stats import power_divergence

# power_divergence(f_obs, f_exp=None, ddof=0, axis=0, lambda_=None, *, nan_policy='propagate', keepdims=False)
```

## Library docstring

```
Cressie-Read power divergence statistic and goodness of fit test.

This function tests the null hypothesis that the categorical data
has the given frequencies, using the Cressie-Read power divergence
statistic.

Parameters
----------
f_obs : array_like
    Observed frequencies in each category.
f_exp : array_like, optional
    Expected frequencies in each category.  By default the categories are
    assumed to be equally likely.
ddof : int, optional
    "Delta degrees of freedom": adjustment to the degrees of freedom
    for the p-value.  The p-value is computed using a chi-squared
    distribution with ``k - 1 - ddof`` degrees of freedom, where `k`
    is the number of observed frequencies.  The default value of `ddof`
    is 0.
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.
lambda_ : float or str, optional
    The power in the Cressie-Read power divergence statistic.  The default
    is 1.  For convenience, `lambda_` may be assigned one of the following
    strings, in which case the corresponding numerical value is used:

    * ``"pearson"`` (value 1)
        Pearson's chi-squared statistic. In this case, the function is
        equivalent to `chisquare`.
    * ``"log-likelihood"`` (value 0)
        Log-likelihood ratio. Also known as the G-test [3]_.
    * ``"freeman-tukey"`` (value -1/2)
        Freeman-Tukey statistic.
    * ``"mod-log-likelihood"`` (value -1)
        Modified log-likelihood ratio.
    * ``"neyman"`` (value -2)
        Neyman's statistic.
    * ``"cressie-read"`` (value 2/3)
        The power recommended in [5]_.
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 
```

## Quick recipe

```python
import scipy.stats as _m
score = _m.power_divergence(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)`.