The reaction rates in the Swedish pressurized water reactors Ringhals 3 and Ringhals 4 are measured with in-core detectors and calculated with a deterministic nodal code. The corresponding residuals (measured values minus calculated values) are used to determine the uncertainty of the maximum rod power, constituting a limiting parameter in-core design and a fundamental parameter in safety analysis. This study aims to make a statistical investigation of the axially averaged reaction rates. Multiple models of the distribution of the residuals are constructed under the assumption of normality by applying phenomenological deduction, kernel density estimations, Box-Cox transformations, multivariate normal distribution, and the Gaussian mixture model. The models are normality, two-sample, and autocorrelation tested with the Shapiro-Wilk test, Kolmogorov-Smirnov test, and Durbin-Watson test, respectively. Ultimately, predictions of the models are compared to new data. The models constructed with kernel density estimations and Box-Cox transformations appear to accurately describe statistical characteristics of the sampled data. However, the data are found to be clustered, position correlated, and autocorrelated, making these models invalid. The multivariate normal distribution applied to the position-specific residuals is, on the other hand, able to predict new data. Results from the Gaussian mixture model support the cycle-based clustering used in the multivariate normal distribution.