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Analysis of rounded exponential data

机译:四舍五入的指数数据

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The problem of inference based on a rounded random sample from the exponential distribution is treated. The main results are given by an explicit expression for the maximum-likelihood estimator, a confidence interval with a guaranteed level of confidence, and a conjugate class of distributions for Bayesian analysis. These results are exemplified on two concrete examples. The large and increasing body of results on the topic of grouped data has been mostly focused on the effect on the estimators. The methods and results for the derivation of confidence intervals here are hence of some general theoretical value as a model approach for other parametric models. The Bayesian credibility interval recommended in cases with a lack of other prior information follows by letting the prior equal the inverted exponential with a scale equal to one divided by the resolution. It is shown that this corresponds to the standard non-informative prior for the scale in the case of non-rounded data. For cases with the absence of explicit prior information it is argued that the inverted exponential prior with a scale given by the resolution is a reasonable choice for more general digitized scale families also.
机译:处理了根据指数分布的四舍五入随机样本进行推理的问题。主要结果由最大似然估计器的显式表达式,具有保证的置信度的置信区间和贝叶斯分析的共轭分布类别给出。这些结果在两个具体示例中得到了例证。关于分组数据主题的大量越来越多的结果主要集中在对估计量的影响上。因此,这里推导置信区间的方法和结果具有一些一般理论价值,可作为其他参数模型的模型方法。在缺少其他先验信息的情况下,建议使用贝叶斯可信区间,其方法是使先验等于倒数指数,小数位数等于分辨率除以1。结果表明,在非四舍五入数据的情况下,这对应于量表的标准非信息先验。对于没有明确的先验信息的情况,有人认为,分辨率给定比例的倒数指数先验对于更一般的数字化比例尺系列也是一个合理的选择。

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