Resampling based inference for a distribution function using censored ranked set samples

Abstract

This article deals with constructing confidence intervals/bands for a distribution function based on censored ranked set samples. Toward this end, a resampling plan is suggested and its validity is investigated. Monte Carlo simulations are used to compare performances of the bootstrap confidence intervals with their asymptotic analogs, and their modifications by jackknife. An environmental data set is finally analyzed.

Appendix

See Tables 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Table 1 Estimated coverage probabilities of 0.95 CIs under model I and $n=12$

Table 2 Estimated coverage probabilities of 0.95 CIs under model I and $n=36$

Table 3 Estimated coverage probabilities of 0.95 CIs under model I and $n=60$

Table 4 Estimated lengths of 0.95 CIs under model I and $n=12$

Table 5 Estimated lengths of 0.95 CIs under model I and $n=36$

Table 6 Estimated lengths of 0.95 CIs under model I and $n=60$

Table 7 Estimated coverage probabilities of 0.95 CBs for F(t) using (12) under model I

Table 8 Estimated coverage probabilities of 0.95 CBs for F(t) using (13) under model I

Table 9 MTBE concentrations (in $\mu$g/l) from ground-water samples collected by RSS with $k=3$ and $m=4$