Systematic errors in the maximum-likelihood regression of Poisson count data: introducing the overdispersed χ2 distribution

This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The is applicable particular X-ray spectra situations where Poisson log-likelihood, or Cash goodness-of-fit statistic, indicate poor fit that attributable overdispersion Overdispersion data treated as an intrinsic model variance can be estimated from best-fit model, using Cmin statistic. also studies effects such on Delta C likelihood-ratio which used test for presence nested component introduces overdispersed chi-square distribution results convolution models usual and zero-mean Gaussian proposed choice statistic errors. methods presented this are applied XMM-Newton quasar 1ES 1553+113 were detect absorption lines intervening warm-hot intergalactic medium (WHIM). case study illustrates how data, their effect detection component, line, with