ExpandingVar

Description

The ExpandingVar function returns the sample variance (delta degrees of freedom ddof=1) of every sample seen since the last reset. It shares the ddof=1 convention with RollingVar and pandas.Series.expanding().var(). Undefined (NaN) until at least two samples have been seen. Memory is O(1).

Equation:

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

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 ExpandingVar

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