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Conservative merging of hypotheses given by probability densities

The paper deals with the merging of hypotheses that are not provided with weights and are represented by probability densities. A recently proposed definition of a conservative probability density is exploited to evolve the ideas of the covariance union approach. It is derived that the solution with the lowest entropy is given by the mixture density with the maximum entropy and a closed form solution for disjoint supports is presented. The proposed approach is also applicable to discrete random variables. The paper is concluded by illustrative examples.