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The calculation of the characteristic function of the signal fluctuations dueto clustered astrophysical sources is performed in this paper. For the typicalcase of power-law differential number counts and two-point angular correlationfunction, we present an extension of Zolotarev's theorem that allows us tocompute the cumulants of the logarithm of the absolute value of the intensity.As a test, simulations based on recent observations of radio galaxies are thencarried out, showing that these cumulants can be very useful for determiningthe fundamental parameters defining the number counts and the correlation. Ifthe angular correlation scale of the observed source population is known, themethod presented here is able to obtain estimators of the amplitude and slopeof the power-law number counts with mean absolute errors that are one order ofmagnitude better than previous techniques, that did not take into account thecorrelation. Even if the scale of correlation is not well known, the method isable to estimate it and still performs much better than if the effect ofcorrelations is not considered.

Confusion noise due to clustered extragalactic point sources. Application of logarithmic cumulants for parameter estimation