A Normal Limit Theorem for Power Sums of Independent Random Variables

Suppose thatpₙ\ = \ 10 log₁₀\ [10^x₁/10 + … + 10^xₙ/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 Pnwill 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.