The multivariate Fermi-Dirac distribution and its applications in quality control View Full Text


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Article Info

DATE

1996-12

AUTHORS

Mauro Gasparini, Peiming Ma

ABSTRACT

We investigate the multivariate elliptically contoured generalization of a parametric family of univariate distributions proposed by Ferreri (1964) for its potential applications in Quality Control. Such ap-variate Fermi-Dirac distribution has density wherex, μ ∈Rp, α ∈R, Σ is ap×p positive definite matrix of rankp and is the Fermi-Dirac integral used in statistical physics. The Fermi-Dirac family provides, through α, a one-dimensional continuous parametrization that joins the multivariate uniform distribution on an ellipsoid to the multivariate normal distribution. A discussion of maximum likelihood estimation of its parameters illustrates some interesting nonstandard phenomena. For example, as a by-product, a possible solution to the problem of circumscribing the smallest ellipsoid to a set of points inRp is obtained. The method is illustrated by a multivariate quality control example. More... »

PAGES

307-322

References to SciGraph publications

  • 1991. Smallest enclosing disks (balls and ellipsoids) in NEW RESULTS AND NEW TRENDS IN COMPUTER SCIENCE
  • 1990. Symmetric Multivariate and Related Distributions in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02589093

    DOI

    http://dx.doi.org/10.1007/bf02589093

    DIMENSIONS

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