ExpandingStd

Description

The ExpandingStd function returns the sample standard deviation (ddof=1) of every sample seen since the last reset; it is the square root of ExpandingVar and matches pandas.Series.expanding().std(). Undefined (NaN) until at least two samples have been seen. Memory is O(1).

Equation:

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

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 ExpandingStd

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