Curvature-standardised Robust Score Estimation for the Gompertz Distribution

Likelihood-based inference for exponential-tail lifetime models can be unstable in finite samples, particularly under right-tail contamination. We develop a robust score-based inference procedure for the two-parameter Gompertz distribution by constructing estimating equations in which influence is bounded after standardisation by the local curvature of the likelihood, implemented via OPG-whitened score contributions and Huber weighting. Uncertainty is quantified using a Godambe (sandwich) covariance estimator, enabling Wald-type inference. Simulation results under clean sampling and controlled right-tail contamination show improved stability and more reliable coverage than maximum likelihood, with a moderate efficiency loss under correct specification.