Structure-preserving mappings of uniform order statistics

Abstract

There are several well-known mappings which transform the first r common order statistics in a sample of size n from a standard uniform distribution to a full vector of dimension r of order statistics in a sample of size r from a uniform distribution. Continuing the results reported in a previous paper by the authors, it is shown that transformations of these types do not lead to order statistics from an i.i.d. sample of random variables, in general, when being applied to order statistics from non-uniform distributions. By accepting the loss of one dimension, a structure-preserving transformation exists for power function distributions.

Keywords:

• order statistics
• goodness-of-fit tests
• transformation of censored samples
• uniform distribution

Acknowledgements

The authors are grateful to the referees for their careful reading, and for helpful comments and suggestions, which led to an improved presentation.