A use of mixtures of two normal distributions in a classification problem
David W. Hosmer · Journal of Statistical Computation and Simulation · 1978
An assumption made in the classification problem is that the distribution of the data being classified has the same parameters as the data used to obtain the discriminant functions. A method based on mixtures of two normal distributions is proposed as method of checking this assumption and modifying the discriminant functions accordingly. As a first step, the case considered in this paper, is that of a shift in the mean of one or two univariate normal distributions with all other parameters remaining fixed and known. Calculations based on the asymptotic the proposed method works well even for small shifts.