Selection of Good Populations and Related Confidence Intervals Using Sample Quasi-Ranges

SYNOPTIC ABSTRACT

We consider k (k≥ 2) independent populations or treatments such that an observation from population π_i follows an absolutely continuous distribution which is a member of a location-scale family with location parameter μ_i (−∞ <μ_i < ∞) and scale parameter θ_i (θ_i > 0), i = l,…,k. For a given δ₁ (δ₁ > 1) the population π_i is considered ‘good’ if θ_i ≤δ₁θ_[1], i = l,…,k, where θ_[1] = min (θ₁,…,θ_k). A class of selection procedures, based on sample quasi-ranges, is proposed to select a subset of k populations which includes all the good populations with probability at least P* (a pre-assigned value). Simultaneous confidence intervals for the ratios of scale parameters, which can be derived with the help of proposed procedures, are discussed. We call population π_i, ‘bad’ if θ_i > δ₂θ_[1] (δ₂ > δ₁, > 1), i = l,…,k. A class of selection procedures is also proposed to guarantee that the probability of either selecting a bad population or omitting a good population is at most 1- P*. The application of the proposed procedures to uniform and two-parameter exponential probability models is discussed, separately, with necessary tables. Finally, a numerical example, based on real life data, is given.

Key Words and Phrases:

• subset selection
• quasi ranges
• outliers
• censored sample
• simultaneous confidence intervals