Multivariate Logistic Mixtures

Abstract

Logistic mixtures, unlike normal mixtures, have not been studied for their topography. In this paper we discuss analogs of some of the multivariate normal mixture results for the multivariate logistic distribution. We focus on graphical techniques that are based on displaying the elevation of the density on the ridgeline. These techniques are quite elementary, and carry full information about the location and relative heights of the modes and saddle points. Moreover, we turn to a technique that names II-Plot which denotes that the first differentiation of the second component density ratios the difference between the first differentiations of the second component density and the first component density.

The Constructive Implicit Function Theorem and Proof in Logistic Mixtures

“…Theorem 1 later frequently allows us to show some ridgeline and contour plots, where the ridgeline function satisfies that the left side of formula (1) is equal to null (see [3]). The following example is in the case of two dimensions and three components.…”