I am interested in a circular equivalent to the classical CLT. Is there a necessary and sufficient condition telling when a normalized sum of circular distributed random variables converges to a WrappedNormal distributed random variable? That is, what conditions do circular i.i.d. random vectors $X_i$ have to satisfy in order to ensure $$\frac{1}{\sqrt{n}} \sum_{i=1}^n X_i \mod 2\pi$$ converges to a WrappedNormal distributed random variable. Is there a similar result for (hyper-)spheres?
2026-03-30 03:58:35.1774843115
Central Limit Theorem on the Circle
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