The Bhattacharyya Matrix for the Mixture of Two Distributions

Abstract

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Application of the characterization theory to the mixture model

“…However, if the Bhattacharyya matrix is diagonal or non-diagonal elements of the matrix are equal, then one can invert it to obtain the corresponding bounds. In discussing the Bhattacharyya matrix for the mixture of two distributions Whittaker (1973) considered the estimation of the parameter 0 in the mixture distribution wheref, and f2 are such that they differ at each point of some set of positive Lebesgue measure (or of positive counting measure in the case of discrete case). Hill (1963) ~ showed that the Cramer-Rao minimum variance bound for an unbiased estimate of 0 for a sample of observations from the above mixture distributive equal 1 where Z(O> = f,(x)X(x) dx and it lies in ( 0~1 ) 0f,(x> + ( 1 -0lf2(~)…”

“…According to Whittaker (1973), the Bhattacharyya matrix for the mixture distribution is given by: Characterization theory and the mixture model 267 normal-normal model, since we are taking mean and variance of fl and fi to be the same, so that the mixture off, and f2 will again be a normal distribution. Also from Kanji (1985), fig.…”