Inference and Prediction for a General Order Statistic Model with Unknown Population Size
总体规模未知的一般次序统计量模型：推断与预测AI 解读 ↓
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总体规模未知的一般次序统计量模型：推断与预测
- 研究问题
- 仅观测未知规模总体样本中的前若干个次序统计量时，如何推断总体规模及分布参数，并预测后续观测？
- 方法与思路
- 作者提出贝叶斯—经验贝叶斯推断框架，以比较可能非嵌套的分布模型，并讨论以极限非正规先验近似模糊先验信息。
- 材料陈述的贡献
- 摘要称，该框架提供易实现的推断与预测程序；三个软件可靠性案例提示指数模型可能过于乐观，Weibull 模型值得考虑。
- 阅读关注点
- 应核对总体规模先验、非正规先验极限下后验是否适定、模型比较规则，以及未来观测和可靠性预测的定义。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；先验与模型条件未详述，软件案例不能支持普遍预测优势，也不能推断刊本变化。
原文摘要
Suppose that the first n order statistics from a random sample of N positive random variables are observed, where N is unknown. This, the general order statistic model, has been applied to the study of market penetration, capture—recapture, burn-in in repairable systems, software reliability growth, the estimation of the number of individuals exposed to radiation, and the estimation of the number of unseen species. Inference is to be made about the unknown parameters, especially N, and future observations are to be predicted. A Bayes empirical Bayes approach to inference is presented. This permits the comparison of competing, perhaps nonnested, models for the distribution of the random variables in a natural way. It also provides easily implemented inference and prediction procedures that avoid the difficulties of non-Bayesian methods. One such difficulty is that the maximum likelihood estimator of N may be infinite. Results are given for the case in which vague prior information about the model parameters is approximated by limiting, improper, prior forms. Applications to three software reliability data sets indicate that the much-used exponential order statistic may give rather optimistic estimates of system reliability and that the not previously considered Weibull order statistic model seems promising for such applications.