Motivated by an engineering pullout test applied to a steel strip embedded in earth, we show how the resulting linearly decreasing force leads naturally to a new distribution, if the force under constant stress is modeled via a three-parameter Weibull. We term this the LDSWeibull distribution, and show that inference on the parameters of the underlying Weibull can be made upon collection of data from such pullout tests. Various classical finite-sample and asymptotic properties of the LDSWeibull are studied, including existence of moments, distribution of extremes, and maximum likelihood based inference under different regimes. The LDSWeibull is shown to have many similarities with the Weibull, but does not suffer from the problem of having an unbounded likelihood function under certain parameter configurations. We demonstrate that the quality of its fit can also be very competitive with that of the Weibull in certain applications.

中文翻译：

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线性降低的应力威布尔（LDSWeibull）：一种新的威布尔式分布

通过对埋在地下的钢带进行工程拉拔试验的启发，我们展示了如果通过三参数Weibull对恒定应力下的力进行建模，则所得的线性减小的力自然会导致新的分布。我们将其称为LDSWeibull分布，并表明可以根据从此类拉出测试收集的数据来推断基础Weibull的参数。研究了LDSWeibull的各种经典有限样本和渐近性质，包括矩的存在，极值的分布以及在不同情况下基于最大似然的推断。LDSWeibull已显示与Weibull有许多相似之处，但在某些参数配置下不存在具有无限似然函数的问题。