Distribution theory for selection from logistic populations

P. Laan, van der

    Research output: Book/ReportReportAcademic

    20 Downloads (Pure)

    Abstract

    Assume k (integer k \geq 2) independent populations \pi_1, \pi_2, ..., \pi_k are given. The associated independent random variables X_1, X_2, ..., X_k are Logistically distributed with unknown means \mu_1, \mu_2, ..., \mu_k, respectively, and common known variance. The goal is to select the best population, this is the population with the largest mean. Some distributional results are derived for subset selection as well as for the indifference zone approach. The probability of correct selection is determined. Exact and numerical results concerning the expected subset size are presented for the subset selection approach. Finally, some remarks are made for a generalized selection goal using subset selection. This goal is to select a non-empty subset of populations that contains at least one \epsilon-best (almost best) treatment with confidence level P*. For a set of populations an \epsilon-best reatment is defined as a treatment with location parameter on a distance less than or equal to \epsilon (\epsilon \geq 0) from the best population.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages12
    Publication statusPublished - 1991

    Publication series

    NameMemorandum COSOR
    Volume9123
    ISSN (Print)0926-4493

    Fingerprint

    Distribution Theory
    Logistics
    Subset Selection
    Pi
    Indifference Zone
    Probability of Correct Selection
    Associated Random Variables
    Subset
    Location Parameter
    Confidence Level
    Independent Random Variables
    Less than or equal to
    Exact Results
    Unknown
    Numerical Results
    Integer

    Cite this

    Laan, van der, P. (1991). Distribution theory for selection from logistic populations. (Memorandum COSOR; Vol. 9123). Eindhoven: Technische Universiteit Eindhoven.
    Laan, van der, P. / Distribution theory for selection from logistic populations. Eindhoven : Technische Universiteit Eindhoven, 1991. 12 p. (Memorandum COSOR).
    @book{a1ecad8afd954c3caa721eb77895fc76,
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    Laan, van der, P 1991, Distribution theory for selection from logistic populations. Memorandum COSOR, vol. 9123, Technische Universiteit Eindhoven, Eindhoven.

    Distribution theory for selection from logistic populations. / Laan, van der, P.

    Eindhoven : Technische Universiteit Eindhoven, 1991. 12 p. (Memorandum COSOR; Vol. 9123).

    Research output: Book/ReportReportAcademic

    TY - BOOK

    T1 - Distribution theory for selection from logistic populations

    AU - Laan, van der, P.

    PY - 1991

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    N2 - Assume k (integer k \geq 2) independent populations \pi_1, \pi_2, ..., \pi_k are given. The associated independent random variables X_1, X_2, ..., X_k are Logistically distributed with unknown means \mu_1, \mu_2, ..., \mu_k, respectively, and common known variance. The goal is to select the best population, this is the population with the largest mean. Some distributional results are derived for subset selection as well as for the indifference zone approach. The probability of correct selection is determined. Exact and numerical results concerning the expected subset size are presented for the subset selection approach. Finally, some remarks are made for a generalized selection goal using subset selection. This goal is to select a non-empty subset of populations that contains at least one \epsilon-best (almost best) treatment with confidence level P*. For a set of populations an \epsilon-best reatment is defined as a treatment with location parameter on a distance less than or equal to \epsilon (\epsilon \geq 0) from the best population.

    AB - Assume k (integer k \geq 2) independent populations \pi_1, \pi_2, ..., \pi_k are given. The associated independent random variables X_1, X_2, ..., X_k are Logistically distributed with unknown means \mu_1, \mu_2, ..., \mu_k, respectively, and common known variance. The goal is to select the best population, this is the population with the largest mean. Some distributional results are derived for subset selection as well as for the indifference zone approach. The probability of correct selection is determined. Exact and numerical results concerning the expected subset size are presented for the subset selection approach. Finally, some remarks are made for a generalized selection goal using subset selection. This goal is to select a non-empty subset of populations that contains at least one \epsilon-best (almost best) treatment with confidence level P*. For a set of populations an \epsilon-best reatment is defined as a treatment with location parameter on a distance less than or equal to \epsilon (\epsilon \geq 0) from the best population.

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    Laan, van der P. Distribution theory for selection from logistic populations. Eindhoven: Technische Universiteit Eindhoven, 1991. 12 p. (Memorandum COSOR).