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This article defines a distribution family based on the distribution of a random variable associated with the projections of a normally distributed random matrix with unknown mean onto a linear space and onto a closed convex cone. The stochastic monotonicity property of the distributions in the family is established. This property finds the application in the proving the unbiasedness of a likelihood ratio test in a multivariate order restricted model.

Stochastic monotonicity of a distribution family associated with matrix projections and its application