Abstract
In this paper, we propose an efficient branch and bound procedure to compute exact nonparametric statistical intervals based on two Type-II right censored data sets. The procedure is based on some recurrence relations for the distribution and density functions of progressively Type-II censored order statistics which can be applied to compute the coverage probabilities. We illustrate the method for both confidence and prediction intervals of a given level.
Similar content being viewed by others
References
Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York
Balakrishnan N (2007) Progressive censoring methodology: an appraisal (with discussions). Test 16: 211–296
Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Birkhäuser, Boston
Balakrishnan N, Beutner E, Cramer E (2010) Exact two-sample non-parametric confidence, prediction, and tolerance intervals based on ordinary and progressively Type-II right censored data. Test 19:68–91
Beutner E, Cramer E (2010) Nonparametric meta-analysis for minimal-repair systems. Aust N Z J Stat 52:383–401
Cramer E (2009) Hermite interpolation polynomials and distributions of ordered data. Stat Methodol 6: 337–343
David HA, Nagaraja HN (2003) Order statistics. Wiley, Hoboken
Hahn GJ, Meeker WQ (1991) Statistical intervals: a guide for practitioners. Wiley, New York
Kamps U, Cramer E (2001) On distributions of generalized order statistics. Statistics 35:269–280
Nelson W (1982) Applied life data analysis. Wiley, New York
Volterman W, Balakrishnan N (2010) Exact nonparametric confidence, prediction and tolerance intervals based on multi-sample Type-II right censored data. J Stat Plan Inference 140:3306–3316
Volterman W, Balakrishnan N, Cramer E (2012) Exact nonparametric meta-analysis for multiple independent doubly Type-II censored samples. Comp Stat Data Anal 56:1243–1255
Wang H (2008) Coverage probability of prediction intervals for discrete random variables. Comput Stat Data Anal 53:17–26
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Balakrishnan, N., Beutner, E. & Cramer, E. Computational aspects of statistical intervals based on two Type-II censored samples. Comput Stat 28, 893–917 (2013). https://doi.org/10.1007/s00180-012-0335-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00180-012-0335-z