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首页> 外文期刊>The American statistician >Simple Estimation Intervals for Poisson, Exponential, and Inverse Gaussian Means Obtained by Symmetrizing the Likelihood Function
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Simple Estimation Intervals for Poisson, Exponential, and Inverse Gaussian Means Obtained by Symmetrizing the Likelihood Function

机译：通过对称似然函数获得的泊松，指数和高斯均值的简单估计区间

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摘要

Likelihood intervals for the Poisson, exponential, and inverse Gaussian means that have simple analytically closed expressions and good coverage frequencies for any sample size are given here explicitly. Their simplicity is striking and they should be more broadly used in applications everywhere. Their soundness is due to three statistical properties that these three distributions share as well as the fact that for all of them there exists a simple power reparameterization that symmetrizes the corresponding likelihood function. As a consequence, asymptotic maximum likelihood results are applicable even for samples of size one. Likelihood intervals of the new parameter may be easily transformed back to the original parameter of interest, the mean, by the invariance property of the likelihood function. Practical examples are given to illustrate the proposed inferential procedures.
机译：此处明确给出了泊松，指数和反高斯方法的似然区间，这些区间具有简单的分析性闭合表达式和任何样本量的良好覆盖频率。它们的简单性引人注目，应在所有应用程序中更广泛地使用它们。它们的健全性归因于这三个分布所共有的三个统计属性，以及对于所有分布都存在简单的幂重新参数化（对称性表示对应的似然函数）的事实。因此，渐近最大似然结果甚至适用于大小为1的样本。通过似然函数的不变性，可以容易地将新参数的似然区间转换回感兴趣的原始参数均值。给出了实际的例子来说明所提出的推理程序。

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