Abstract
The first-order probability density of sums of sine waves having random phases and amplitudes is approximated using a method developed by H. E. Daniels [Ann. Math. Stat. 25, No. 4, 631–650 (Dec. 1954)]. Three cases are discussed: (1) random phase and equal amplitude, (2) random phase and sine-distributed amplitudes, and (3) random phase and rectangularly distributed amplitudes. Detailed results are presented for the first two cases. It is shown that extremal statistics may be quite poorly estimated by an assumption of normality.
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