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Injectivity of real rational mappings: The case of a mixture of two Gaussian laws

Daniel Lazard 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Using methods from computer algebra, especially Gröbner bases, we study the application which maps the mixtures of two Gaussian laws of probability to their six first moments. It is proved that the mapping is injective, and thus that the parameters of the mixture may be recovered from the values of the moments. This method of proof may be applied to many physical problems where there are more measured variables than the state variables to be recovered.
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Submitted on : Tuesday, September 26, 2006 - 10:13:52 AM
Last modification on : Friday, February 4, 2022 - 3:33:31 AM

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Daniel Lazard. Injectivity of real rational mappings: The case of a mixture of two Gaussian laws. Mathematics and Computers in Simulation, Elsevier, 2004, 67 (1-2), pp.67--84. ⟨inria-00100070⟩

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