A normal limit theorem for power sums of independent random variables

Suppose that
$p_{n}\ = \ 10 {\rm log}_{10}\ [10^{x_{1}/10} + \ldots + 10^{x_{n}/10}]$,$
where {X
n
} is a sequence of independent random variables. The main result of this paper shows that under very general conditions on the sequence {X
n
}, the power sums P
n
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.