# dask.array.stats.kurtosis

### dask.array.stats.kurtosis(a, axis=0, fisher=True, bias=True, nan_policy='propagate')

Compute the kurtosis (Fisher or Pearson) of a dataset.

This docstring was copied from scipy.stats.kurtosis.

Some inconsistencies with the Dask version may exist.

Kurtosis is the fourth central moment divided by the square of the
variance. If Fisher’s definition is used, then 3.0 is subtracted from
the result to give 0.0 for a normal distribution.

If bias is False then the kurtosis is calculated using k statistics to
eliminate bias coming from biased moment estimators

Use kurtosistest to see if result is close enough to normal.

* **Parameters:**
  **a**
  : Data for which the kurtosis is calculated.

  **axis**
  : 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.

  **fisher**
  : If True, Fisher’s definition is used (normal ==> 0.0). If False,
    Pearson’s definition is used (normal ==> 3.0).

  **bias**
  : If False, then the calculations are corrected for statistical bias.

  **nan_policy**
  : 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**
  : 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:**
  **kurtosis**
  : The kurtosis of values along an axis, returning NaN where all values
    are equal.

### Notes

Beginning in SciPy 1.9, `np.matrix` inputs (not recommended for new
code) are converted to `np.ndarray` before the calculation is performed. In
this case, the output will be a scalar or `np.ndarray` of appropriate shape
rather than a 2D `np.matrix`. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or `np.ndarray` rather than a
masked array with `mask=False`.

**Array API Standard Support**

kurtosis has experimental support for Python Array API Standard compatible
backends in addition to NumPy. Please consider testing these features
by setting an environment variable `SCIPY_ARRAY_API=1` and providing
CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following
combinations of backend and device (or other capability) are supported.

| Library   | CPU   | GPU   |
|-----------|-------|-------|
| NumPy     | ✅    | n/a   |
| CuPy      | n/a   | ✅    |
| PyTorch   | ✅    | ✅    |
| JAX       | ✅    | ✅    |
| Dask      | ✅    | n/a   |

kurtosis also accepts [MArrays](https://mdhaber.github.io/marray/tutorial.html) backed by the backends indicated above; masked values will be treated as though they were not present.

See [Support for the array API standard](https://docs.scipy.org/doc/scipy/dev/api-dev/array_api.html#dev-arrayapi) for more information.

### References

### Examples

In Fisher’s definition, the kurtosis of the normal distribution is zero.
In the following example, the kurtosis is close to zero, because it was
calculated from the dataset, not from the continuous distribution.

```pycon
>>> import numpy as np
>>> from scipy.stats import norm, kurtosis
>>> data = norm.rvs(size=1000, random_state=3)
>>> kurtosis(data)
-0.06928694200380558
```

The distribution with a higher kurtosis has a heavier tail.
The zero valued kurtosis of the normal distribution in Fisher’s definition
can serve as a reference point.

```pycon
>>> import matplotlib.pyplot as plt
>>> import scipy.stats as stats
>>> from scipy.stats import kurtosis
```

```pycon
>>> x = np.linspace(-5, 5, 100)
>>> ax = plt.subplot()
>>> distnames = ['laplace', 'norm', 'uniform']
```

```pycon
>>> for distname in distnames:
...     if distname == 'uniform':
...         dist = getattr(stats, distname)(loc=-2, scale=4)
...     else:
...         dist = getattr(stats, distname)
...     data = dist.rvs(size=1000)
...     kur = kurtosis(data, fisher=True)
...     y = dist.pdf(x)
...     ax.plot(x, y, label="{}, {}".format(distname, round(kur, 3)))
...     ax.legend()
```

The Laplace distribution has a heavier tail than the normal distribution.
The uniform distribution (which has negative kurtosis) has the thinnest
tail.

<!-- !! processed by numpydoc !! -->