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Exact Non‐Parametric Confidence, Prediction and Tolerance Intervals with Progressive Type‐II Censoring

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  • Olivier Guilbaud

Abstract

. This article extends recent results [Scand. J. Statist. 28 (2001) 699] about exact non‐parametric inferences based on order statistics with progressive type‐II censoring. The extension lies in that non‐parametric inferences are now covered where the dependence between involved order statistics cannot be circumvented. These inferences include: (a) tolerance intervals containing at least a specified proportion of the parent distribution, (b) prediction intervals containing at least a specified number of observations in a future sample, and (c) outer and/or inner confidence intervals for a quantile interval of the parent distribution. The inferences are valid for any parent distribution with continuous distribution function. The key result shows how the probability of an event involving k dependent order statistics that are observable/uncensored with progressive type‐II censoring can be represented as a mixture with known weights of corresponding probabilities involving k dependent ordinary order statistics. Further applications/developments concerning exact Kolmogorov‐type confidence regions are indicated.

Suggested Citation

  • Olivier Guilbaud, 2004. "Exact Non‐Parametric Confidence, Prediction and Tolerance Intervals with Progressive Type‐II Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 265-281, June.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:2:p:265-281
    DOI: 10.1111/j.1467-9469.2004.02-119.x
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    Cited by:

    1. Olivier Guilbaud, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 279-281, August.
    2. Ahmadi, Jafar & MirMostafaee, S.M.T.K. & Balakrishnan, N., 2010. "Nonparametric prediction intervals for future record intervals based on order statistics," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1663-1672, November.
    3. Alvarez-Andrade, S. & Balakrishnan, N. & Bordes, L., 2007. "Homogeneity tests based on several progressively Type-II censored samples," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1195-1213, July.
    4. Ahmadi, J. & Balakrishnan, N., 2005. "Distribution-free confidence intervals for quantile intervals based on current records," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 190-202, December.
    5. Beutner, E. & Cramer, E., 2014. "Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 95-109.

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