Unbiased Simultaneous Prediction Limits on Future Order Statistics with Applications

Abstract

Statistical prediction is the earliest and most prevalent form of statistical inference. It is the provision of an estimate, usually in the one-sided or two-sided interval form, for future observations based on the results obtained from past observations. In particular, the minimum, maximum, mean, median of a future sample or ranges of given number of samples could also be aims of prediction. Prediction has its uses in a variety of disciplines such as medicine, engineering and business. In this paper, we consider the problems of constructing unbiased simultaneous prediction limits on the order statistics of all of k future samples using the results of a previous sample from the same underlying distribution belonging to invariant family. The prediction limits obtained in the paper are generalizations of the usual prediction limits on observations or functions of observations of only one future sample. Attention is restricted to invariant families of distributions. The technique used here emphasizes pivotal quantities relevant for obtaining ancillary statistics and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. It does not require the construction of any tables and is applicable whether the data are complete or Type II censored. Applications of the proposed procedures are given for the two-parameter exponential and Weibull distributions. The proposed technique is conceptually simple and easy to use. The exact prediction limits are found and illustrated using some practical examples. Index Terms — Future samples of observations, order statistics, simultaneous prediction limits

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Cite this paper

@inproceedings{Nechval2013UnbiasedSP, title={Unbiased Simultaneous Prediction Limits on Future Order Statistics with Applications}, author={Nicholas A. Nechval}, year={2013} }