In this paper, we suggest a novel method for detecting mortality deceleration. We focus on the gamma-Gompertz frailty model and suggest the subtraction of a penalty in the log-likelihood function as an alternative to traditional likelihood inference and hypothesis testing. Over existing methods, our method offers advantages, such as avoiding the use of a p-value, hypothesis testing, and asymptotic distributions. We evaluate the performance of our approach by comparing it with traditional likelihood inference on both simulated and real mortality data. Results have shown that our approach is more accurate in detecting mortality deceleration and provides more reliable estimates of the underlying parameters. The proposed method is a significant contribution to the literature as it offers a powerful tool for analyzing mortality patterns.

翻译：本文提出了一种检测死亡率减速的新方法。我们聚焦于伽马-冈珀茨脆弱模型，并提出在对数似然函数中减去一个惩罚项，作为传统似然推断和假设检验的替代方案。与现有方法相比，我们的方法具有优势，例如避免使用p值、假设检验和渐近分布。我们通过将本方法与模拟和真实死亡率数据上的传统似然推断进行比较，评估了其性能。结果表明，我们的方法在检测死亡率减速方面更为准确，并提供了更可靠的基础参数估计。所提出的方法为文献做出了重要贡献，因为它为分析死亡率模式提供了一种强有力的工具。