[BUG] Fix incorrect variance calculation and capability tagging in Hurdle

[ANANYA542]

Reference Issues/PRs

fixes #972

What does this implement/fix? Explain your changes.

This PR fixes an issue in the Hurdle distribution where the variance was being computed incorrectly.
The current implementation uses p * var_positive + p * (1 - p) * mean_positive, but the mean term should be squared. This was leading to significant underestimation of the variance. The formula has been corrected to use (mean_positive ** 2) in line with the law of total variance.

I also updated how capability tags are determined. Previously, Hurdle checked the base distribution to decide whether mean/var are exact, but since it internally wraps the distribution using LeftTruncated, those values are actually computed via numerical approximation. The tags now reflect this correctly by checking the truncated distribution instead.

Does your contribution introduce a new dependency? If yes, which one?

No

What should a reviewer concentrate their feedback on?

• Whether the updated variance formula aligns with expected behavior across different base distributions
• Whether capability tagging should consistently be based on the internally used truncated distribution

Did you add any tests for the change?

I verified the fix using Monte Carlo simulation (100k samples), where the empirical variance now matches the analytical result within tolerance. No new formal unit tests have been added yet.

Any other comments?

A screenshot showing the before/after behavior has also been added for clarity.

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[ANANYA542]

Hi @fkiraly — just following up on this PR. If you could take some time to review it and let me know if any changes or explanation is required, I’d really appreciate it.