Generalized Confidence Intervals

Weerahandi, Samaradasa

doi:10.1007/978-1-4612-0825-9_6

Cited by 108 publications

(69 citation statements)

References 14 publications

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“…The concept of generalized p-value was introduced by Tsui and Weerahandi (1989) for hypothesis testing. Weerahandi (1993) extended the idea for constructing confidence intervals. The book by Weerahandi (1995b) gives a detailed discussion along with numerous examples.…”

Section: Introductionmentioning

confidence: 99%

Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method

Krishnamoorthy¹,

2003

Biometrics

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Summary. This article presents procedures for hypothesis testing and interval estimation of the common mean of several normal populations. The methods are based on the concepts of generalized p-value and generalized confidence limit. The merits of the proposed methods are evaluated numerically and compared with those of the existing methods. Numerical studies show that the new procedures are accurate and perform better than the existing methods when the sample sizes are moderate and the number of populations is four or less. If the number of populations is five or more, then the generalized variable method performs much better than the existing methods regardless of the sample sizes. The generalized variable method and other existing methods are illustrated using two examples.

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Section: Introductionmentioning

confidence: 99%

Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method

Krishnamoorthy¹,

2003

Biometrics

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“…We refer to Hannig 21 for a detailed discussion of the approach. The concept of a fiducial interval was introduced earlier in Weerahandi 22 under the name generalized confidence interval . However, for the present problems, based on estimated coverage probabilities, our recommendation is the fiducial approach and the bootstrap‐calibrated delta method; our overall recommendation is in favor of the the latter.…”

Section: Discussionmentioning

confidence: 99%

Tolerance limits under zero‐inflated lognormal and gamma distributions

Zimmer

Park

Mathew

2020

Comp and Math Methods

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The computation of upper tolerance limits is investigated for the zero‐inflated lognormal distribution and the zero‐inflated gamma distribution, with or without covariates. The methodologies investigated consist of a fiducial approach and bootstrap approaches, including the bias corrected and accelerated bootstrap and a bootstrap‐calibrated delta method. Based on estimated coverage probabilities, it is concluded that overall, the bootstrap‐calibrated delta method is to be preferred for computing the upper tolerance limit. Two applications are also discussed; the first application is on the analysis of data on health care expenditures, and the second application is on testing the safety of body armor.

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“…By the FGCI definition, the first condition (FGCI1) is that the distribution of FGPQ is free of all unknown parameters, and the second one (FGCI2) indicates the observed value of FGPQ equals to the parameter of interest. Additionally, the FGCI is a subclass of GPQ of Weerahandi (1993), importantly it is stronger point than GCI for condition (FGCI2). Recently, the existing FGCI for delta‐lognormal mean of Hasan and Krishnamoorthy (2018) provided a good performance.…”

Section: Cis For the Difference Of Variancesmentioning

confidence: 99%