Resumen de Some Multiple Comparisons Using Sample Quasi Ranges on Censored Data
A. N. Gill, Parminder Singh
We consider $k(k \ge 2)$ independent populations (treatments or systems) and an absolutely continuous member of location-scale family of distributions, index by the location parameter $\mu _i ({ - \infty < \mu _i < \infty } )$ and scale parameter $\theta _i ({\theta _i > 0}), $ is used to model the observations from the ith population, $ i = 1,...,k .$ The problem of simultaneous selection of two subsets, one containing population associated with the smallest $ \theta $ - value and other containing population with the largest $ \theta $ - value with probability at least a pre-specified value $P^*({\frac{1}{{k(k-1)}} < P^* < 1}) $ is considered when the data are censored. We also construct $100P^*\%$ simultaneous upper and two-sided confidence intervals for $ \frac{{\theta _{[i]}}}{{\theta _[1]}}},i = 2,...,k,\frac{{\theta _{[k]} }}{{\theta _{[i]}}},i = 1,...,k - 1, $ where $ \theta _{[1]} \le .... \le \theta _{[k]} $ denotes the ordered values of $\theta s.$ The proposed procedures, based on sample quasi ranges, are useful when the experimenter has smaller samples or censored samples or there is suspicion of outliers in the samples. The results are applied to exponential populations model and, for this case: (i) the constants have been computed to apply the proposed multiple comparisons; (ii) two members of the proposed class have been compared with the existing procedure. A numerical example is also given.
