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非中心卡方分布非中心参数的估计AI 解读

Let $X$ be distributed according to a non-central Chi squared distribution with $p$ degrees of freedom. The non-central Chi squared distribution arises in various statistical analyses and the estimation of the non-centrality parameter is of importance in some problems. This paper deals with the admissibility of certain estimates of the non-centrality parameter. It is shown that $(X - p)^+$, the positive part of $X - p$ dominates the maximum likelihood estimator with squared…

估计最大总体均值的单次抽样程序AI 解读

A single-sample procedure is proposed for obtaining asymptotically optimum confidence intervals for the largest mean of k normal populations with common unknown variance.

有序位置或尺度参数的区间估计与同时选择AI 解读

A formulation is given and a procedure is proposed for constructing a confidence interval for a certain ordered location or scale parameter and for simultaneously selecting all populations having parameters equal or larger than this ordered parameter with a preassigned minimal probability. The well-known indifference-zone formulation of the ranking problem is obtained as a special case as is the problem of interval estimation of an ordered parameter.

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…

多个分布中最大 α 分位数的无分布区间估计AI 解读

A procedure based on order statistics is given for the interval estimation of the largest α-quantile of several continuous distributions. Results on infimum of coverage probability are obtained for one-sided and two-sided intervals. An optimality criterion is proposed and an algorithm is given for two-sided intervals. Large sample approximations are also considered.

摘要暂缺

多个正态总体中最大方差的区间估计AI 解读

A procedure is given for obtaining a random width confidence interval for the largest variance of k normal populations. The determination of the sample size to achieve a preassigned confidence coefficient can be done by the use of chisquare tables only.

摘要暂缺

已知方差的多个正态总体最大均值的区间估计AI 解读

A procedure is given for the construction of a fixed-width confidence interval of the largest mean of k(k≥1) normal populations with a common known variance, based on the largest sample mean. The sample size required to achieve the preassigned confidence coefficient can be computed by using the standard normal table only.

摘要暂缺