Add std to fitters.py

[LeonidElkin]

Add characteristic std

Naming convention: "std".

std denotes the standard deviation of a random variable:
std(X) = sqrt(Var(X)).

1. Relation to variance

Standard deviation is defined as the square root of variance:

• std(X) = sqrt(var(X))
• var(X) = central_moment(order=2)

No independent statistical computation logic should be implemented inside std.

All mathematical logic for obtaining dispersion-related quantities must live in:

• central_moment(order=2) (primary definition),
• and/or var (as its thin wrapper).

std must be implemented strictly as a thin wrapper over var, applying an elementwise square root.

There must be no alternative computational paths that bypass var.

2. Integration into the characteristic graph

• Register std as a node in the global characteristic graph.
• Add a single edge:
  • var -> std

The planner must obtain std exclusively via var.

No direct edges from:

• central_moment,
• raw_moment,
• pdf,
• pmf,
• or any other characteristic

should exist.

3. Implementation requirements

• The implementation must support NumPy array semantics.
• The square root must be applied elementwise.
• Behavior for negative numerical noise (e.g., tiny negative values due to floating-point errors) must be defined:
  • Either clamp small negative values to zero within tolerance,
  • Or raise a well-defined error (decision must be consistent with var policy).

The behavior must be explicitly tested.

4. Tests

Add tests that verify:

• std equals sqrt(var) for analytical distributions.
• For at least one distribution:
  • std matches the analytical standard deviation (within tolerance).
  • std equals sqrt(central_moment(order=2)) via the graph.
• Array semantics:
  • Scalar input,
  • Vector input,
  • Broadcasting behavior (if applicable).