Mixtures and Characteristic Functions

Characteristic functions of scale mixtures of multivariate skew-normal distributions

Characteristic Functions and Averages

Let Ω be a set and Ω1, . . . ,Ωm−1 subsets of Ω, being m an integer greater than one. For a given function f = (f1, . . . fm) : Ω → R, we prove the existence of a unique function α = (α1, . . . , αm) : Ω → R m such that

Mixtures of receiver operating characteristic curves.

RATIONALE AND OBJECTIVES Receiver operating characteristic (ROC) curves are ubiquitous in the analysis of imaging metrics as markers of both diagnosis and prognosis. While empirical estimation of ROC curves remains the most popular method, there are several reasons to consider smooth estimates based on a parametric model. MATERIALS AND METHODS A mixture model is considered for modeling the di...

Lecture 10: Characteristic Functions

1.1 Complex random variables 1.2 Definition and basic properties of characteristic functions 1.3 Examples 1.4 Inversion formulas 2. Applications 2.1 Characteristic function for sum of independent random variables 2.2 Characteristic functions and moments of random variables 2.3 Continuity theorem 2.4 Weak law of large numbers 2.5 Central Limit theorem 2.6 Law of small numbers 1. Definition of ch...

Characteristic Functions for Ergodic Tuples

Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G.Popescu. We prove that our characteristic function is a complete unitary invariant for such tuples and show how it can be computed. Mathematics Subject Classific...