Abstract

A single outlier sequence in which the distribution of the first observation differs from the others is considered and the properties of record statistics extracted from such sequence are studied. The problem of estimating the model parameters is discussed in the proportional hazard rate model. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are obtained for the special case of exponential distribution. The best linear unbiased (invariant) estimator is also derived for the location-scale family of distributions and their efficiencies are calculated. The problems of predicting the future records and reconstructing the past records are investigated. Various predictors and reconstructors are presented and some of their properties are stated. The precision of the obtained predictors are compared based on both the mean squared prediction error and Pitman’s measure of closeness criteria. Finally, an example with real data is given to illustrate the results.

摘要

考虑第一个观测值的分布不同于其他观测值的单个异常值序列，并研究从该序列中提取的记录统计信息的属性。在比例风险率模型中讨论了估计模型参数的问题。对于指数分布的特殊情况，获得了最大似然估计器和一致最小方差无偏估计器。还针对位置尺度分布族推导了最佳线性无偏（不变）估计量，并计算了它们的效率。研究了预测未来记录和重建过去记录的问题。介绍了各种预测器和重构器，并说明了它们的一些特性。基于均方预测误差和接近度标准的Pitman度量，比较获得的预测变量的精度。最后，给出一个带有实际数据的例子来说明结果。