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

Daniel Lazard (1)

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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.

Mots clés: identification of parameters; melange de gaussiennes; méthode des moments; identification de paramètres; mixture of gaussian laws; application of computer algebra; rational mapping; method of the moments; application du calcul formel; application rationelle

Domaines: Autre [cs.OH]

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