Stabilize Complex Watson fitting for extreme weights#4393
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Summary
float64limitBug
ComplexWatsonDistribution.estimate_parameterspreviously evaluated bothsum(weights)andZ * weights[:, None]at the caller's raw scale. Individually finite weights could therefore overflow in the reduction or matrix product. For example, weights proportional to[8, 4, 2, 1]but scaled so the largest value isfloat64.maxproduced an infinite total and aNaNscatter matrix, even though common weight scaling must not change the estimate.Fix
Normalize weights by their largest value before computing the total and weighted scatter. The scaled weights lie in
[0, 1]; their sum and weighted samples remain bounded, while the final normalization is algebraically identical to the original formula.Validation
tests/distributions/test_complex_watson_extreme_weights.py, checking phase-invariant mean direction and concentration parameter equalitymain, zero behind; changes one production file and adds one focused regression test