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排序参数的区间估计AI 解读

Summary Let F(x; θ) denote a family of distributions on the real line, indexed by the real-valued parameter θ. It is assumed that the given family is stochastically increasing in θ, that is, F(x; θ) is non-increasing in θ for each x. Let θ l …, θk represent k unknown values of the parameter θ, and let X l …, Xk represent k independent observations from the distributions F(x; θ l), …, F(x; θk), respectively. Let X* and θ* denote the ith smallest values among the observations…

最大参数的最优置信区间AI 解读

There are given k univariate distributions, indexed by a real-valued parameter θ, and k independent observations, one from each distribution. Let θ* denote the largest among the values of θ associated with the given distributions. This article is concerned with the estimation of θ*. A class of confidence intervals and a subclass of “optimal” confidence intervals for θ* are given. For a general class of distributions it is shown that the coverage probability of the confidence…