Concept About Estimated Standard Deviation
Given data $ { \left\{ {x}_{i} \right\} }_{i = 1}^{N} $ the Empirical STD of the data is well defined:

$$ STD = \sqrt{ \frac{1}{N - 1} \sum_{i = 1}^{N} { \left( {x}_{i} - \bar{x} \right) }^{2} } $$

Where $ \bar{x} $ is the empirical mean of the data given by:

$$ \bar{x} = \frac{1}{N} \sum_{i = 1}^{N} {x}_{i} $$

Now, if there's a model on the data (Such as signal and noise with certain CDF) the empirical calculation should be altered accordingly.  

For instance, given a signal which is linear with AWGN the STD of the noise can be estimated by removing the linear estimated signal first.