ExpandingKurt

Description

The ExpandingKurt function returns the bias-corrected Fisher excess kurtosis of every sample seen since the last reset, using the same estimator as RollingKurt and pandas.Series.expanding().kurt(). Undefined (NaN) until at least four samples have been seen. Memory is O(1).

Equation:

\[ y[t] = \frac{n(n+1)}{(n-1)(n-2)(n-3)}\sum_{i=0}^{t}\left(\frac{x[i]-\bar{x}}{s}\right)^4 - \frac{3(n-1)^2}{(n-2)(n-3)}, \quad n=t+1 \]

Parameters: none.

NaN handling

Policy: ignore. A NaN in the input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples

Usage example

import numpy as np
from screamer import ExpandingKurt

x = np.arange(1.0, 11.0)
y = ExpandingKurt()(x)