Extreme and rare changes in space mission solar irradiance records are scientifically relevant but difficult to quantify because these records are finite, instrument dependent, and affected by observational gaps and time varying measurement quality. We evaluated extreme daily logarithmic changes in the band integrated 0.1-7.0 nm irradiance measured by photodiode 7 of the Solar Radiation and Climate Experiment/X-Ray Photometer System (SORCE/XPS) from 2005 to 2019. After constructing a regular daily series by linear interpolation, we analyzed daily logarithmic changes in irradiance and fitted stationary Generalized Extreme Value models to 60 day block maxima and transformed 15 day block minima. Block lengths were selected using Ljung-Box diagnostics and sample autocorrelation functions. Maximum likelihood estimation was used as the primary inferential method, with probability weighted moments as a sensitivity check. The maximum likelihood GEV shape estimates were 0.1661 for maxima and 0.2928 for transformed minima, with closely aligned estimates under the two fitting methods. These positive point estimates are compatible with Fréchet type tails under the selected block constructions. Annualized return levels provide interpretable summaries of extreme relative increases and reductions, but estimates for long return periods remain strongly dependent on extrapolation beyond the 15 year record. Reported measurement precision and absolute uncertainty were used to qualify the interpretation of the fitted tails and were not propagated through the likelihood. By combining EVT based tail modeling with explicit consideration of measurement precision, absolute uncertainty, interpolation, and mission data gaps, the analysis provides an uncertainty aware astrostatistical baseline for extreme value inference from processed solar mission records.

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