In geometry of n dimensions, an orthant is one of the 2n parts of Euclidean space defined by given conditions on the Cartesian coordinates, that they are positive or negative. That is, an orthant is the analogue of a quadrant in the plane, and is defined by a system of inequalities
A leading case of such an integral is the negative orthant probability, where B = {v
The multinomial probit (MNP) model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities, with ยต and depending on unknown parameters (and, in general, on covariates).
Estimation of this model requires, for each trial parameter vector and each observation in a sample, evaluation of P(mu;B) and of its derivatives with respect to mu and Omega.
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