 Tail integral formula for moments

ID: tail-integral-formula-for-moments

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

q > 0

X

with finite absolute

q

th moment, Tonelli theorem gives

E ∣ X ∣^{q} = q \int_{0}^{\infty} t^{q - 1} P (∣ X ∣ \geq t) d t .

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