Power sum distributions arise in communications noise and highway noise models. Inverse Gaussian or Wald distributions with the same index of dispersion are similar and infinitely divisible, and often closely approximate lognormal distributions, and, thus, are more suitable than lognormals for theoretical studies. The Wald distribution is an exact model for Poisson distributed point sources with Erlang (O) emissions of noise power.
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Allan H. Marcus (1976) studied this question.
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