Quantile-Oriented Sensitivity Analysis Using a Hermite Model Based on Four Moments

Quantile-oriented sensitivity analysis (QOSA) requires repeated evaluation of conditional quantiles over many conditioning states. A four-moment Hermite model yields closed-form quantiles, but its published two-branch form has a local admissibility gap for small nonzero skewness near the Gaussian kurtosis. A coefficient-anchored continuation provides a narrow operational completion around this gap while retaining the published lower and upper branches elsewhere, thereby preventing conditional moment states within the gap from interrupting the calculation of the QOSA indices. The completed quantile is then used in a lower conditional tail expectation (LCTE) procedure for first-order and total QOSA indices. In a mildly non-Gaussian example, the estimated indices agreed closely with their analytical values, and an engineering comparison reproduced the previously reported dominant first-order effects. For a strongly skewed lognormal response, the input ranking remained correct, but the index values were inaccurate and the Hermite approximation did not adequately reproduce the target tail. A heuristic tail-hardness indicator Hp is introduced as an initial warning of difficult approximation regimes. Comparisons with direct Monte Carlo, kernel, and random-forest QOSA reveal distinct computational trade-offs. The results support the use of the Hermite–LCTE procedure for mildly non-Gaussian responses with stable moment estimates and an adequately approximated target tail.