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The Resource An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource)
An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource)
Resource Information
The item An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 Let X1, X2 ..., X[subscript n] be independent, pdimensional random vectors and let there exist nonsingular p x p matrices A1 ..., A[subscript n], B1 ..., B[subscript n], such that the random vectors A1X1 + ... + A[subscript n]X[subscript n] and B1X1 + ... + B[subscript n]X[subscript n] are stochastically independent. Then the X[subscript i] are normally distributed. This result is proved by discussing functional equation: [sigma] 1 <̲ i <̲ n f[subscript i](t + c[subscript i]u) = A(tu) + B(ut), where t, u are pdimensional vectors, the c[subscript i] are nonsingular matries and A(xy), B(xy) are polynomials in x, for each fixed pvector
 Language
 eng
 Extent
 11 pages
 Note

 July 21, 1961
 Contract number AF 49 (638)  877
 Label
 An extension of the functional equation of skitovich characterizing the multivaraite normal distribution
 Title
 An extension of the functional equation of skitovich characterizing the multivaraite normal distribution
 Statement of responsibility
 S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota
 Language
 eng
 Summary
 Let X1, X2 ..., X[subscript n] be independent, pdimensional random vectors and let there exist nonsingular p x p matrices A1 ..., A[subscript n], B1 ..., B[subscript n], such that the random vectors A1X1 + ... + A[subscript n]X[subscript n] and B1X1 + ... + B[subscript n]X[subscript n] are stochastically independent. Then the X[subscript i] are normally distributed. This result is proved by discussing functional equation: [sigma] 1 <̲ i <̲ n f[subscript i](t + c[subscript i]u) = A(tu) + B(ut), where t, u are pdimensional vectors, the c[subscript i] are nonsingular matries and A(xy), B(xy) are polynomials in x, for each fixed pvector
 Cataloging source
 OCLCE
 http://bibfra.me/vocab/lite/collectionName
 Technical Report Archive & Image Library (TRAIL)
 http://library.link/vocab/creatorName
 Ghurye, S. G
 Government publication
 federal national government publication
 Index
 no index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 technical reports
 http://library.link/vocab/relatedWorkOrContributorName

 Northwestern University (Evanston, Ill.)
 University of Minnesota
 United States
 Series statement
 Air Force Office of Scientific Research
 Series volume
 AFOSR 901
 http://library.link/vocab/subjectName

 Functional equations
 Matrices
 Gaussian distribution
 Label
 An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource)
 Note

 July 21, 1961
 Contract number AF 49 (638)  877
 Antecedent source
 file reproduced from original
 Bibliography note
 Includes bibliographical references
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Dimensions
 28 cm.
 Dimensions
 unknown
 Extent
 11 pages
 File format
 one file format
 Form of item
 online
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Specific material designation
 remote
 System control number

 (OCoLC)1103319963
 (OCoLC)on1103319963
 Label
 An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource)
 Note

 July 21, 1961
 Contract number AF 49 (638)  877
 Antecedent source
 file reproduced from original
 Bibliography note
 Includes bibliographical references
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Dimensions
 28 cm.
 Dimensions
 unknown
 Extent
 11 pages
 File format
 one file format
 Form of item
 online
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Specific material designation
 remote
 System control number

 (OCoLC)1103319963
 (OCoLC)on1103319963
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/Anextensionofthefunctionalequationof/_LpQVM8WHY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/Anextensionofthefunctionalequationof/_LpQVM8WHY/">An extension of the functional equation of skitovich characterizing the multivaraite normal distribution, S.G. Ghurye, Northwestern University, Ingram Olkin, University of Minnesota, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>