skip to content
Sufficient conditions for association of binary variables. Preview this item
ClosePreview this item
Checking...

Sufficient conditions for association of binary variables.

Author: D W Walkup; BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB.
Publisher: Ft. Belvoir Defense Technical Information Center DEC 1966.
Edition/Format:   Print book : English
Summary:
In connection with studies of reliability of coherent binary systems, it has been suggested that a set of binary random variables be called associated if all pairs of binary nondecreasing functions of these variables have nonnegative covariance. In this note it is shown that there exists a unique smallest set A of pairs of binary nondecreasing functions on the variables such that nonnegative covariance for the pairs  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: D W Walkup; BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB.
OCLC Number: 227440850
Description: 22 pages

Abstract:

In connection with studies of reliability of coherent binary systems, it has been suggested that a set of binary random variables be called associated if all pairs of binary nondecreasing functions of these variables have nonnegative covariance. In this note it is shown that there exists a unique smallest set A of pairs of binary nondecreasing functions on the variables such that nonnegative covariance for the pairs in A is necessary and sufficient condition for association of the variables. This set A is characterized and it is shown that its size increases rapidly with the number of variables. It is also shown that for four or more variables there exist pairs in A corresponding to coherent systems with no nontrivial modules, thus suggesting it is impossible to find an equivalent definition of association of binary random variables which makes material use of partitioning of the variables. (Author).

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/227440850> # Sufficient conditions for association of binary variables.
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "227440850" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/vau> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/137166641#Place/ft_belvoir> ; # Ft. Belvoir
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/mfg_&_industrial_eng_&_control_of_product_sys> ; # Mfg & Industrial Eng & Control of Product Sys
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/mathematical_logic> ; # Mathematical logic
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/set_theory> ; # (Set theory
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/reliability> ; # Reliability
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/combinatorial_analysis> ; # Combinatorial analysis
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/theoretical_mathematics> ; # Theoretical Mathematics
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/binary_arithmetic> ; # (Binary arithmetic
   schema:about <http://experiment.worldcat.org/entity/work/data/137166641#Topic/random_variables> ; # Random variables)
   schema:bookFormat bgn:PrintBook ;
   schema:contributor <http://experiment.worldcat.org/entity/work/data/137166641#Person/walkup_d_w> ; # D. W. Walkup
   schema:contributor <http://experiment.worldcat.org/entity/work/data/137166641#Organization/boeing_scientific_research_labs_seattle_wash_mathematics_research_lab> ; # BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB.
   schema:datePublished "1966" ;
   schema:datePublished "DEC 1966" ;
   schema:description "In connection with studies of reliability of coherent binary systems, it has been suggested that a set of binary random variables be called associated if all pairs of binary nondecreasing functions of these variables have nonnegative covariance. In this note it is shown that there exists a unique smallest set A of pairs of binary nondecreasing functions on the variables such that nonnegative covariance for the pairs in A is necessary and sufficient condition for association of the variables. This set A is characterized and it is shown that its size increases rapidly with the number of variables. It is also shown that for four or more variables there exist pairs in A corresponding to coherent systems with no nontrivial modules, thus suggesting it is impossible to find an equivalent definition of association of binary random variables which makes material use of partitioning of the variables. (Author)."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/137166641> ;
   schema:inLanguage "en" ;
   schema:name "Sufficient conditions for association of binary variables."@en ;
   schema:productID "227440850" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/227440850#PublicationEvent/ft_belvoirdefense_technical_information_centerdec_1966> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/137166641#Agent/defense_technical_information_center> ; # Defense Technical Information Center
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/227440850> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/137166641#Agent/defense_technical_information_center> # Defense Technical Information Center
    a bgn:Agent ;
   schema:name "Defense Technical Information Center" ;
    .

<http://experiment.worldcat.org/entity/work/data/137166641#Organization/boeing_scientific_research_labs_seattle_wash_mathematics_research_lab> # BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB.
    a schema:Organization ;
   schema:name "BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB." ;
    .

<http://experiment.worldcat.org/entity/work/data/137166641#Person/walkup_d_w> # D. W. Walkup
    a schema:Person ;
   schema:familyName "Walkup" ;
   schema:givenName "D. W." ;
   schema:name "D. W. Walkup" ;
    .

<http://experiment.worldcat.org/entity/work/data/137166641#Topic/binary_arithmetic> # (Binary arithmetic
    a schema:Intangible ;
   schema:name "(Binary arithmetic"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/137166641#Topic/combinatorial_analysis> # Combinatorial analysis
    a schema:Intangible ;
   schema:name "Combinatorial analysis"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/137166641#Topic/mfg_&_industrial_eng_&_control_of_product_sys> # Mfg & Industrial Eng & Control of Product Sys
    a schema:Intangible ;
   schema:name "Mfg & Industrial Eng & Control of Product Sys"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/137166641#Topic/theoretical_mathematics> # Theoretical Mathematics
    a schema:Intangible ;
   schema:name "Theoretical Mathematics"@en ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.