In this paper, we consider interval estimation for the inverse Gaussian (IG) distribution. Using generalized pivotal quantity method, we derive the generalized confidence intervals (GCIs) for the model parameters and some quantities such as the quantile, the reliability function of the lifetime, the failure rate function, and the mean residual lifetime. We verify that the GCI of the scale parameter is the same as its commonly used exact CI. We also obtain the generalized prediction intervals (GPIs) for future failure times based on the observed failure data set. In addition, we get the GCI for the reliability of the stress–strength model when the stress and strength variables follow the IG distributions with different parameters. We compare the proposed GCIs and GPIs with the Wald CIs and bootstrap- $p$ CIs by simulation. The simulation results show that the proposed GCIs and GPIs are superior to the Wald CIs and the bootstrap-p CIs in terms of the coverage probability. Finally, two examples are used to illustrate the proposed procedures.

中文翻译：

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逆高斯分布的区间估计

在本文中，我们考虑逆高斯 (IG) 分布的区间估计。使用广义关键量方法，我们推导出模型参数和一些量的广义置信区间（GCI），例如分位数、寿命的可靠性函数、失效率函数和平均剩余寿命。我们验证了尺度参数的 GCI 与其常用的精确 CI 相同。我们还根据观察到的故障数据集获得了未来故障时间的广义预测区间 (GPI)。此外，当应力和强度变量遵循具有不同参数的 IG 分布时，我们得到了应力-强度模型可靠性的 GCI。我们将提议的 GCI 和 GPI 与 Wald CI 和引导程序进行比较$磷$模拟的 CI。仿真结果表明，所提出的 GCI 和 GPI在覆盖概率方面优于 Wald CI 和 bootstrap- p CI。最后，使用两个例子来说明所提出的程序。