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A normal limit theorem for power sums of independent random variables

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Suppose that p_{n} = 10 {\rm \log }_{10} [10^{x_{1}/10} + \ldots + 10^{x_{n}/10}]$, where {Xn} is a sequence of independent random variables. The main result of this paper shows that under very general conditions on the sequence {Xn}, the power sums Pn will be asymptotically normally distributed. This result supports a commonly used normal approximation, and shows why many physical quantities obtained by power addition of random variables tend to be normally distributed in dB.

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The Bell System Technical Journal  (Volume:46 ,  Issue: 9 )