Higher-order statistical analysis of inter-arrival times for radiation detector deadtime characterization and paralysis factor determination

All real detectors exhibit hybrid behavior that combines both paralyzable and non-paralyzable which requires improved characterization techniques. This study investigates the relationship between detector deadtime parameters and higher-order statistical for inter-arrival time distributions to develop advanced detector characterization. Two comprehensive Monte Carlo simulation approaches were employed using MATLAB: a full radioactive decay curve analysis spanning approximately 4.5 half-lives of Cobalt-60 and Vanadium-52 sources, and a fixed count rate analysis covering practically achievable laboratory conditions (440 to 1,000,000 counts per second). The hybrid deadtime model was implemented with deadtimes ranging from 2.5 to 50 μs for the full simulation and from 2.5 to 30 μs for the fixed count rate study and paralysis factors from 0.1 to 0.99 and from 0.1 to 0.4 for the fixed count rate study. Statistical measures including coefficient of variation (CV), skewness, and kurtosis of inter-arrival time distributions were calculated across 200 simulation runs for decay analysis and 50 independent runs for fixed count rate measurements. The results revealed distinct sensitivity patterns among statistical measures to detector parameters. Coefficient of variation demonstrated strong dependence on paralysis factor with an exponential relationship PF=0.0015e^(12.657CV), R² = 0.9998, enabling direct determination of paralysis factor. This work demonstrates that higher-order statistical analysis of inter-arrival times contains valuable diagnostic information typically discarded in conventional counting statistics, opening new possibilities for automated detector characterization and real-time performance assessment in radiation detection systems offering significant advantages for quality assurance, calibration verification, and performance monitoring applications.