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Journal of Probability and Statistics
Volume 2016, Article ID 8246390, 5 pages
http://dx.doi.org/10.1155/2016/8246390
Research Article

Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values

1Department of Statistics, Daejeon University, No. 62, Daehak-ro, Dong-gu, Republic of Korea
2Department of Statistics, Yeungnam University, No. 280, Daehak-ro, Gyeongsan, Republic of Korea

Received 22 July 2016; Revised 20 October 2016; Accepted 8 November 2016

Academic Editor: Shesh N. Rai

Copyright © 2016 Jung-In Seo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data.