Information matrix for a mixture of two normal distributions

This paper presents a numerical method for computation of the Fisher information matrix about the five parameters of a mixture of two normal distributions. It is shown, by using a simple transformation which reduces the number of parameters from five to three, that the computation of the whole information matrix leads to the numerical evaluation of a particular integral. The Hermite-Gauss quadrature formula, Romberg's algorithm, a power series, and Taylor's expansion are applied for the evaluation of this integral and the results are compared with each other. A short table has been provided from which the approximate information matrix can be obtained in practice.