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Volterman, William; Balakrishnan, N.; Cramer, Erhard

Exact nonparametric meta-analysis for multiple independent doubly type-II censored samples. (English) Zbl 1241.62071

Comput. Stat. Data Anal. 56, No. 5, 1243-1255 (2012).
Summary: Nonparametric inferential methods are discussed for the situation of multiple independent doubly Type-II censored samples. The basic distribution theory for the pooled sample is given assuming that the underlying distribution is continuous and it is demonstrated how the weights in the mixture representations of the pooled order statistics as a mixture of the usual order statistics can be obtained. This is used to construct nonparametric prediction intervals, tolerance intervals for a future sample, and confidence intervals for a population quantile. A small simulation study compares the exact coverage probabilities for population quantiles, to those obtained where the mixture weights are generated by simulation.

Cited in 8 Documents

MSC:

62G15 Nonparametric tolerance and confidence regions
62N01 Censored data models
62G30 Order statistics; empirical distribution functions
62E15 Exact distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)

Keywords:

nonparametric confidence intervals; nonparametric prediction intervals; nonparametric tolerance intervals; mixtures; pooled samples
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References:

[1] Arnold, B. C.; Balakrishnan, N.; Nagaraja, H. N., A First Course in Order Statistics (1992), John Wiley & Sons: John Wiley & Sons New York · Zbl 0850.62008
[2] Balakrishnan, N.; Beutner, E.; Cramer, E., Exact two-sample non-parametric confidence, prediction, and tolerance intervals based on ordinary and progressively Type-II right censored data, TEST, 19, 68-91 (2010) · Zbl 1203.62089
[3] Balakrishnan, N., Beutner, E., Cramer, E., 2011. Computational aspects of statistical intervals based on two Type-II censored samples (submitted for publication).; Balakrishnan, N., Beutner, E., Cramer, E., 2011. Computational aspects of statistical intervals based on two Type-II censored samples (submitted for publication). · Zbl 1305.65023
[4] Balakrishnan, N.; Cohen, A. C., Order Statistics: Estimation Methods (1991), Academic Press: Academic Press Boston · Zbl 0732.62044
[5] Balakrishnan, N.; Lin, C. T., Exact inference and prediction for \(k\)-sample exponential case under Type-II censoring, Journal of Statistical Computation and Simulation, 75, 5, 315-331 (2005) · Zbl 1061.62043
[6] Balakrishnan, N.; Lin, C. T.; Chan, P. S., Exact inference and prediction for \(k\)-sample two-parameter exponential case under general Type-II censoring, Journal of Statistical Computation and Simulation, 74, 12, 867-878 (2004) · Zbl 1053.62109
[7] Beutner, E.; Cramer, E., A nonparametric meta-analysis for minimal repair systems, Australian and New Zealand Journal of Statistics, 52, 4, 383-401 (2010) · Zbl 1373.62490
[8] David, H. A.; Nagaraja, H. N., Order Statistics (2003), John Wiley & Sons: John Wiley & Sons Hoboken, New Jersey · Zbl 1053.62060
[9] Kim, C.; Han, K., Estimation of the scale parameter of the Rayleigh distribution with multiply type-II censored sample, Journal of Statistical Computation and Simulation, 79, 8, 965-976 (2009) · Zbl 1183.62170
[10] Maurer, W.; Margolin, B. H., The multivariate inclusion-exclusion formula and order statistis from dependent variates, Annals of Statistics, 4, 1190-1199 (1976) · Zbl 0351.62034
[11] Ozturk, O.; Deshpande, J. V., Ranked-set sample nonparametric quantile confidence intervals, Journal of Statistical Planning and Inference, 136, 570-577 (2006) · Zbl 1077.62037
[12] Singh, U.; Gupta, P. K.; Upadhyay, S., Estimation of parameters for exponentiated-Weibull family under Type-II censoring scheme, Computational Statistics & Data Analysis, 48, 3, 509-523 (2005) · Zbl 1429.62453
[13] Sun, X.; Zhou, X.; Wang, J., Confidence intervals for the scale parameter of exponential distribution based on type ii doubly censored samples, Journal of Statistical Planning and Inference, 138, 7, 2045-2058 (2008) · Zbl 1134.62020
[14] Volterman, W.; Balakrishnan, N., Exact nonparametric confidence, prediction, and tolerance intervals based on multi-sample Type-II right censored data, Journal of Statistical Planning and Inference, 140, 11, 3306-3316 (2010) · Zbl 1204.62081
[15] Wu, S.-F., Interval estimation for a Pareto distribution based on a doubly type II censored sample, Computational Statistics & Data Analysis, 52, 7, 3779-3788 (2008) · Zbl 1452.62240
[16] Wu, S.-F.; Yu, Y.-R., The simultaneous confidence intervals for all distances from the extreme populations for two-parameter exponential populations based on the multiply type ii censored samples, Journal of Statistical Computation and Simulation, 81, 2, 137-165 (2011) · Zbl 1206.62042
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