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

Olivier Guilbaud

Scandinavian Journal of Statistics, 2004, vol. 31, issue 2, 265-281

Abstract: 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.

Date: 2004
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