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

## TL;DR

This paper develops a method using logarithmic cumulants to estimate parameters of clustered extragalactic sources affecting confusion noise, improving accuracy over previous techniques by accounting for source correlations.

## Contribution

It extends Zolotarev's theorem to compute cumulants of the logarithm of intensity, enabling better parameter estimation for clustered source populations.

## Key findings

- Cumulants effectively determine number count parameters and correlation scale.
- Method outperforms previous techniques by an order of magnitude in accuracy.
- Estimates remain robust even with uncertain correlation scale.

## Abstract

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