Outer and inner prediction intervals for order statistics intervals based on current records

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• 作者：Jafar Ahmadi (1) ahmadi-j@um.ac.ir
  N. Balakrishnan (234) bala@mcmaster.ca
• 关键词：Beta (gamma) function &#8211 ; Coverage probability &#8211 ; Record coverage &#8211 ; Record range &#8211 ; Spacing &#8211 ; Distribution ; free intervals
• 刊名：Statistical Papers
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：53
• 期：3
• 页码：789-802
• 全文大小：187.5 KB
• 参考文献：1. Ahmadi J, Balakrishnan N (2005) Distribution-free confidence intervals for quantile intervals based on current records. Stat Probab Lett 75: 190–202
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• 作者单位：1. Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, P. O. Box 91775-1159, Mashhad, Iran2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada3. Visiting Professor of King Saud University, Riyadh, Saudi Arabia4. National Center University, Jhongli, Taiwan
• ISSN：1613-9798

文摘

This paper considers the largest and smallest observations at the times when a new record of either kind (upper or lower) occurs. These are called the upper and lower current records and are denoted by Rl_m{R^l_m} and Rs_m{R^s_m}, respectively. The interval (Rs_m,Rl_m){(R^s_m,R^l_m)} is then referred to as the record coverage. The prediction problem in the two-sample case is then discussed and, specifically, the exact outer and inner prediction intervals are derived for order statistics intervals from an independent future Y-sample based on the m-th record coverage from the X-sequence when the underlying distribution of the two samples are the same. The coverage probabilities of these intervals are exact and do not depend on the underlying distribution. Distribution-free prediction intervals as well as upper and lower prediction limits for spacings from a future Y-sample are obtained in terms of the record range from the X-sequence.