Core-dominated non-Gaussian photometric redshifts in the COSMOS field: a normality test analysis

We present a statistical analysis of normalized photometric redshift residuals for 751 radio-selected star-forming galaxies in the COSMOS field. The sample is based on COSMOS2015/UltraVISTA photometric redshifts and is cross-matched with spectroscopic redshifts from the zCOSMOS, LEGA-C surveys, and the COSMOS Spectroscopic Redshift Compilation DR1.1. Four complementary normality tests (Shapiro–Wilk, Kolmogorov–Smirnov, Anderson–Darling, and D’Agostino–Pearson) applied to the normalized residual η ≡ Δz/(1 + zspec) independently reject the Gaussian hypothesis. The residual distribution has a narrow central component (NMAD = 0.013) but a much larger standard deviation (σ = 0.047), reflecting extended tails together with a catastrophic outlier fraction of 1.86 per cent. Removing all 14 catastrophic outliers leaves an outlier-clipped sample of 737 galaxies that still rejects normality (W = 0.895, p = 4.7 × 10−22) with substantial excess kurtosis (γ2 = 6.05), showing that the observed non-Gaussianity is not confined to catastrophic residuals but is also present in the residual core. Sensitivity analyses using secure spectroscopic subsamples and interior-redshift selections consistently reject Gaussianity while leaving the NMAD stable. The strength of the distribution tails varies with sample selection but does not alter the principal result. Replacing the photometric redshifts with those of COSMOS2020 changes the robust scatter by 37 per cent but leaves these conclusions unchanged. Maximum-likelihood model comparison favours the Student-t distribution over both the Gaussian (ΔAIC = 1057) and generalized Gaussian (ΔAIC = 61.5). Conventional summary metrics such as the NMAD and catastrophic outlier fraction alone are therefore insufficient to characterize photometric redshift residual distributions.