Two-Stage and One-Stage Subset Selection Procedures for Exponential Populations under Heteroscedasticity | Chapter 6 | Mathematics and Computer Science: Contemporary Developments Vol. 8

This paper investigates subset selection procedures for k (k \(\ge\) 2) independent populations, where each population follows a two-parameter exponential distribution E(\(\mu\)i, \(\theta\)i) with unknown and possibly unequal location \(\mu\)i and scale \(\theta\)i parameters. We define a set of good populations, G = (i \(\mu\)i \(\ge\) \(\mu\)[k] - \(\epsilon\)1) where \(\mu\)[k]  is the maximum location parameter and \(\epsilon\)1 > 0. The goal is to select a subset S of k populations that contains G with a pre-specified probability P*, i.e., P\(\underline{\delta}\) = (G \(\subseteq\) S| under the proposed procedure)\(\ge\) P*\(\forall\)\(\underline{\delta}\)\(\in\)\(\Omega\), where \(\underline{\delta}\) = (\(\mu\)1, ... , \(\mu\)k, \(\theta\)1, ... , \(\theta\)k) \(\in\) Rk X \(R^k_+\) = \(\Omega\). The paper proposes both two-stage and one-stage subset selection procedures and derives simultaneous confidence intervals for the differences in location parameters \(\mu\)[k] - \(\mu\)i, i = 1, ... ,k and [j]-[i],ij=1,. . . ,k. Further, a subset selection procedure is also introduced to control the probability of omitting a "good" population or selecting a "bad" one, defined by B= (i \(\mu\)i \(\le\) \(\mu\)[k] - \(\epsilon\)2), where \(\epsilon\)2 > \(\epsilon\)1, at1 - P* . The implementation of the proposed procedures is demonstrated using real-life data.

 

Author (s) Details

 

Anju Goyal
Department of Statistics, Panjab University, Chandigarh, India.

 

Amar Nath Gill
School of Basic Sciences, IIIT, Una, H.P., India.

 

Vishal Maurya
Department of Statistics and Information Management, RBI, Mumbai, India.

 

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