On the distribution of the studentized maximum of equally correlated normal random variables

Gupta, Shanti S.; Panchapakesan, S.; Sohn, Joong Kweon

doi:10.1080/03610918508812429

Cited by 34 publications

(10 citation statements)

References 10 publications

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“…Using Hartley's solution (obtained using the theory of characteristics), Gupta obtained an approximation for P ( d ; ν) in powers of 1/ν and remarked that it can be computed by using the Gauss–Hermite quadrature. Gupta et al (1985) extended this result for any ρ > 0 and showed that P ( d ) satisfies in this case too. In this case the approximation for P ( d ) in powers of 1/ν is where L k is the k ‐th correction term and G is the joint cdf of a p ‐variate normal distribution with zero means, common variance σ 2 , and the equicorrelation structure r i j =ρ, i ≠ j .…”

Section: Gupta and Sobel's Probability Integralsmentioning

confidence: 75%

Probability Integrals of the MultivariatetDistribution

Nadarajah¹,

Kotz

2007

Int Statistical Rev

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Results on probability integrals of multivariate t distributions are reviewed. The results discussed include: Dunnett and Sobel's probability integrals, Gupta and Sobel's probability integrals, John's probability integrals, Amos and Bulgren's probability integrals, Steffens' non-central probabilities, Dutt's probability integrals, Amos' probability integral, Fujikoshi's probability integrals, probabilities of cone, probabilities of convex polyhedra, probabilities of linear inequalities, maximum probability content, and Monte Carlo evaluation.

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Section: Gupta and Sobel's Probability Integralsmentioning

confidence: 75%

Probability Integrals of the MultivariatetDistribution

Nadarajah¹,

Kotz

2007

Int Statistical Rev

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“…Lower Bound for Probability of Krishnaiah and Armitage (1966) and of Gupta, Panchapakesan and Sohn (1985). These last tables have P(v) (d) values equal k,l to .…”

Section: Examplementioning

confidence: 97%

Predicted Bounds for Location Parameters of Selected Populations

Bofinger

1986

American Journal of Mathematical and Management Sciences

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SYNOPTIC ABSTRACTAfter selecting t out of k populations (in terms of location) attempts are sometimes made to evaluate the selection process by forming estimates of the probability of correct selection. A more useful evaluation may be done by putting bounds (in a probability sense) on differences (in the location parameters) between (a) the worst selected and the best not selected .or (b) the best selected and the best not selected or (c) the average selected and the average not selected. For these quantities general results (for continuous distributions) are derived and particular results are found for normal distributions with unknown (but equal) variances.

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“…A detailed account of tables available from different sources can be found in Gupta and Panchapakesan (1979, chap. 23, sec. 3) and Gupta et al (1985).…”

Section: Sobel: a Selection And Ranking Pioneermentioning

confidence: 98%

A Personal Tribute to Milton Sobel: Selecting the Best Treatment

Mukhopadhyay

2006

Sequential Analysis

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The paper begins with a sketch of Milton Sobel's life and work, which is followed by a summary of his pioneering collaborations in selecting the best among k ≥2 populations. It takes us back to Bechhofer et al. (1954), where a path-breaking two-stage selection methodology was developed for normal populations with unknown means and a common but unknown variance.Every two-stage methodology begins with a pilot sample. However, no easy practical approach existed for determining an appropriate pilot size until recently. We have summarized two recent ideas to determine a pilot size.Then, the methodology of Bechhofer et al. (1954) is extended for situations where population variances are c 2 i 2 with 2 >0 being unknown but c i >0 being known, not all equal, i = 1 k ≥2 . This new methodology does not need any new statistical table for its implementation beyond what was required by the original 1954 methodology.Several illustrations are included from practical problems using real data. The paper ends with brief recollections of Milton Sobel and some personal thoughts.

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On the distribution of the studentized maximum of equally correlated normal random variables

Cited by 34 publications

References 10 publications

Probability Integrals of the MultivariatetDistribution

Probability Integrals of the MultivariatetDistribution

Predicted Bounds for Location Parameters of Selected Populations

A Personal Tribute to Milton Sobel: Selecting the Best Treatment

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