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

Gasparini, Mauro; Ma, Peiming

doi:10.1007/bf02589093

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…(see Appendix G). A similar PDF has been proposed by Gasparini and Ma [23]: the multivariate Fermi-Dirac distribution defined as the form of…”

Section: 4mentioning

confidence: 70%

Flat-topped Probability Density Functions for Mixture Models

Fujita¹

2022

Preprint

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This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the viewpoint of computational tractability, the PDF based on the Fermi-Dirac or logistic function is advantageous in estimating its shape parameters. The most appropriate PDF for n-variate distribution is of the form:where x, m ∈ R n , Σ is an n × n positive definite matrix, and r > 0 is a shape parameter. The flat-topped PDFs can be used as a component of mixture models in machine learning to improve goodness of fit and make a model as simple as possible.

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“…(see Appendix G). A similar PDF has been proposed by Gasparini and Ma [23]: the multivariate Fermi-Dirac distribution defined as the form of…”

Section: 4mentioning

confidence: 70%

Flat-topped Probability Density Functions for Mixture Models

Fujita¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…They are most often associated with the study of transport phenomena of conductors and semi-conductors [1][2][3][4]. However they also find applications in the seemingly unrelated field of multivariate quality control [5]. The scientific literature, spanning about a century, is replete with papers devoted the study of FermiDirac integrals.…”

Section: Introductionmentioning

confidence: 99%

The Open Mathematics Journal

Selvaggi¹

2012

TOMATJ

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This paper presents a derivation for analytically evaluating the half-order Fermi-Dirac integrals. A complete analytical derivation of the Fermi-Dirac integral of order 1 2 is developed and then generalized to yield each half-order Femi-Dirac function. The most important step in evaluating the Fermi-Dirac integral is to rewrite the integral in terms of two convergent real convolution integrals. Once this done, the Fermi-Dirac integral can put into a form in which a proper contour of integration can be chosen in the complex plane. The application of the theorem of residues reduces the FermiDirac integral into one which becomes analytically tractable. The final solution is written in terms of the complementary and imaginary Error functions.

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

Cited by 2 publications

References 7 publications

Flat-topped Probability Density Functions for Mixture Models

Flat-topped Probability Density Functions for Mixture Models

The Open Mathematics Journal

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