Total positivity order and the normal distribution

Sorting Orders, Subword Complexes, Bruhat Order and Total Positivity

In this note we construct a poset map from a Boolean algebra to the Bruhat order which unveils an interesting connection between subword complexes, sorting orders, and certain totally nonnegative spaces. This relationship gives a simple new proof that the proper part of Bruhat order is homotopy equivalent to the proper part of a Boolean algebra — that is, to a sphere. We also obtain a geometric...

Prediction in a Trivariate Normal Distribution via Two Order Statistics

In this paper, assuming that (X, Y1, Y2)T has a trivariate normal distribution, we derive the exact joint distribution of ( X, Y(1), Y(2))^T, where Y(1) and Y(2) are order statistics arising from (Y1, Y2)T . We show that this joint distribution is a mixture of truncated trivariate normal distributions and then use this mixture representation to derive the best (nonlinear) predictiors of X...

Regulators and Total Positivity

The classical regulator R of a number field K is given [F1] by a rapidly convergent series of the form R w = ∞

Total Positivity and Convexity Preservation

It is well established that systems of totally positive blending functions, such as the Bernstein and B-spline bases, preserve monotonicity and convexity and are generally ‘shape preserving’ [9 ]. In this paper we show that total positivity is equivalent to the preservation of all orders of convexity. By a system we understand a sequence of functions (u0, . . . , un) defined on an interval [a, ...

Sign variation, the Grassmannian, and total positivity