Ratios Involving Extreme Values

Free Extreme Values

Free probability analogues of the basics of extreme value theory are obtained, based on Ando’s spectral order. This includes classification of freely max-stable laws and their domains of attraction, using “free extremal convolutions” on the distributions. These laws coincide with the limit laws in the classical peaks-over-threshold approach. A free extremal projection-valued process over a meas...

Chemical Trees with Extreme Values of Zagreb Indices and Coindices

We give sharp upper bounds on the Zagreb indices and lower bounds on the Zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

Sensitivity, specificity, predictive values, and likelihood ratios.

EXTREME VALUES OF arg L ( 1 , χ )

Values of Dirichlet L-functions at s = 1 have always attracted great attention due to their central role in number theory. In particular the prime number theorem for arithmetic progressions relies on the non-vanishing of L(1, χ) for any non-principal character χ (mod q). Moreover improving the existing lower bounds for |L(1, χ)| (the famous Siegel’s bound |L(1, χ)| ≫ǫ q) would imply many import...

Pooling Peripheral Information: Averages Versus Extreme Values*

Suppose, as an idealization, that sensory intensity is coded in peripheral channels as identical Poisson pulse trains with intensity parameter a power function of signal intensity. Discrimination models based on either an average count computed over a fixed time or an average time computed for a fixed count per channel have difEculty in fitting the Weber function (AI/I versus I) if the free par...