A simple proof of an identity of Good
Published online by Cambridge University Press: 24 October 2008
Extract
Recently, Good discovered the following curious identity (1). Let θ be a real-valued random variable having cumulants Km ≡ Km(θ) (m = 1, 2, …). Take a set of m statistically independent variables θ(1), θ(2), …, θ(m), each with the same distribution as θ, and form the random variable
where ω is any primitive mth root of unity (e.g. ω = e2πi/m). Then
where 〈.〉 denotes expectation.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 183 - 184
- Copyright
- Copyright © Cambridge Philosophical Society 1977
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