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Total positivity order and the normal distribution

Abstract : Unlike the usual stochastic order, total positivity order is closed under conditioning. Here we provide a general formulation of the preservation properties of the order under conditioning; we study certain properties of the order including translation properties and the implications of having equality in the inequality defining the order. Specializing to the multivariate normal distribution, the study of total positivity order leads to new cones defined in terms of covariance M-matrices related to positive dependence, whose properties we study.
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Submitted on : Tuesday, November 23, 2010 - 4:34:02 PM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

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Marco Scarsini, Yosef Rinott. Total positivity order and the normal distribution. Journal of Multivariate Analysis, Elsevier, 2006, Vol.97, N° 5, pp.1251-1261. ⟨10.1016/j.jmva.2005.07.008⟩. ⟨hal-00538990⟩

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