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A new long-term lifetime distribution induced by a latent complementary risk framework

机译：由潜在的互补风险框架引起的新的长期寿命分布

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摘要

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.
机译：在本文中，我们提出了由潜在的互补风险框架（具有递减的，递增的和单峰的危险函数），长期互补指数几何分布引起的新的三参数长期寿命分布。新的分布来自潜在的竞争风险场景，在这种场景下，与生命周期相关的场景（具有特定风险）无法观察到，而是我们仅观察到所有风险中的最大生命周期值以及长期生存。讨论了所提议的分布的性质，包括其概率密度函数以及关于其可靠性，危险性和分位数函数以及阶次统计量的显式代数公式。参数估计基于通常的最大似然法。仿真研究评估估计过程的性能。我们将新分布与其特殊情况以及在三个真实数据集上的长期威布尔分布进行了比较，与常规的长期寿命分布相比，观察了其潜力和竞争力。

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