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    Central Tolerance Regions and Reference Regions for Some Normal Populations

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    24554.pdf (758.1Kb)
    Permanent Link
    http://hdl.handle.net/11603/1001
    Collections
    • UMBC Graduate School
    • UMBC Mathematics and Statistics Department
    • UMBC Student Collection
    • UMBC Theses and Dissertations
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    Author/Creator
    Unknown author
    Date
    2011-01-01
    Type of Work
    application/pdf
    Text
    dissertations
    Department
    Mathematics and Statistics
    Program
    Statistics
    Rights
    This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
    Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.
    Subjects
    Central tolerance factor
    Central tolerance region
    Multivariate normal
    Random effect model
    Reference region
    Simultaneous central tolerance interval
    Abstract
    A reference interval represents a range of values that a physician can use in order to interpret a single test result from a patient. A 95% reference interval is simply the interval from the 2.5th to the 97.5th percentiles of the distribution of the test result. Since such an interval will typically depend on unknown parameters, we can use a random sample to compute an interval that will contain the reference interval with a specified confidence level. The interval so computed is referred to as a central tolerance interval. A central tolerance interval captures, with a given confidence level, a specified percentage of the central part of a univariate population. Reference regions and central tolerance regions are similarly defined for a multivariate population. This thesis considers the problem of deriving central tolerance intervals and regions for some normal populations, including multivariate normal distribution, multivariate linear regression model and the one-way and two-way random models. We also numerically investigate the computation of a simultaneous central tolerance interval for simple linear regression. Simultaneous hypotheses testing of two percentiles is a related problem of interest. The test is usually carried out using two one-sided tests which can be quite conservative. We make an attempt to derive a less conservative test by applying the bootstrap methodology. Numerical examples and real data applications are given to illustrate all of the proposed procedures.


    Albin O. Kuhn Library & Gallery
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    www.umbc.edu/scholarworks

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    Phone: 410-455-3021


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3021


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.