An integrated formulation for selecting the best normal population: the common and unknown variance case

Chen, Pinyuen; Zhang, Jun Lue

doi:10.1080/03610929708832073

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(2 citation statements)

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“…, and c are chosen to satisfy the probability requirement (5). They are the solutions of the following integral equations: When k = 2, for given n 0 and specification (δ * , P * 1 , P * 2 , a), the h * 1 , and h * 2 values simultaneously satisfy:…”

Section: Procedures P Ementioning

confidence: 99%

“…This paper studies the integrated approach in selecting the best normal mean among k normal populations with unequal and unknown variances. Unlike the case of common and unknown variance studied in Chen and Zhang (1997), we can not use the pooled sample variance to estimate the unknown variances in this case. One important change, compared to the case of common and unknown variance, is that in the case of unequal and unknown variances we use weighted averages as the estimators for the population means.…”

Section: Introductionmentioning

confidence: 99%

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An Integrated Selection Formulation for the Best Normal Mean: The Unequal and Unknown Variance Case

Chen¹,

Zhang²

2002

J. of Appl. Math & Decision Sc.

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This paper considers an integrated formulation in selecting the best normal mean in the case of unequal and unknown variances. The formulation separates the parameter space into two disjoint parts, the preference zone (P Z) and the indifference zone (IZ). In the P Z we insist on selecting the best for a correct selection (CS 1) but in the IZ we define any selected subset to be correct (CS 2) if it contains the best population. We find the least favorable configuration (LF C) and the worst configuration (W C) respectively in P Z and IZ. We derive formulas for P (CS 1 |LF C), P (CS 2 |W C) and the bounds for the expected sample size E(N). We also give tables for the procedure parameters to implement the proposed procedure. An example is given to illustrate how to apply the procedure and how to use the table.

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Section: Procedures P Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%