Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the parameters and Kolmogorov-Smirnov type statistics. Simple explicit representations for the boundaries and for the coverage probabilities of the confidence bands are analytically derived, and the performance of the bands is compared in terms of band width and area by means of a data example. As a by-product, a novel confidence region for the location-scale parameter is obtained. Extensions of the results to related models for ordered data, such as sequential order statistics, as well as to other underlying location-scale families of distributions are discussed.
翻译:根据从位置和规模参数不明的指数分布中逐步抽取的第二类审查抽样,通过使用信任区进行参数和Kolmogorov-Smirnov类型统计,为基本分布功能提出了信任带;分析得出信任带边界和覆盖面概率的简单明确表述,以数据为例,按频带宽度和面积比较波段的性能;作为副产品,为位置尺度参数获得新的信任区;讨论将结果扩展至定购数据的相关模型,如顺序顺序统计,以及分布的其他基本位置范围组。