# Kurtosis¶

Running kurtosis using Welford's algorithm.

## Parameters¶

• bias – defaults to False

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

• name

## Examples¶

>>> from river import stats
>>> import scipy.stats
>>> import numpy as np

>>> np.random.seed(42)
>>> X = np.random.normal(loc=0, scale=1, size=10)

>>> kurtosis = stats.Kurtosis(bias=False)
>>> for x in X:
...     print(kurtosis.update(x).get())
-3.0
-2.0
-1.5
1.4130027920707047
0.15367976585756438
0.46142633246812653
-1.620647789230658
-1.3540178492487054
-1.2310268787102745
-0.9490372374384453

>>> for i in range(2, len(X)+1):
...     print(scipy.stats.kurtosis(X[:i], bias=False))
-2.0
-1.4999999999999998
1.4130027920707082
0.15367976585756082
0.46142633246812403
-1.620647789230658
-1.3540178492487063
-1.2310268787102738
-0.9490372374384459

>>> kurtosis = stats.Kurtosis(bias=True)
>>> for x in X:
...     print(kurtosis.update(x).get())
-3.0
-2.0
-1.5
-1.011599627723906
-0.9615800585356089
-0.6989395431537853
-1.4252699121794408
-1.311437071070812
-1.246289111322894
-1.082283689864171

>>> for i in range(2, len(X)+1):
...     print(scipy.stats.kurtosis(X[:i], bias=True))
-2.0
-1.4999999999999998
-1.0115996277239057
-0.9615800585356098
-0.6989395431537861
-1.425269912179441
-1.3114370710708125
-1.2462891113228936
-1.0822836898641714


## Methods¶

get

Return the current value of the statistic.

update

Update and return the called instance.

Parameters

• x (numbers.Number)