Injectivity of real rational mappings: the case of a mixture of two Gaussian laws Original Research Article

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.