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.
Highlights
There is the work by Ray and Lindsay ([6]) on the key features of multivariate normal mixtures, including the determination of the number of modes and general modality theorems
We have proposed a technique for the topography of multivariate logistic mixtures
This is performed by the ridgeline function x∗(α) and the Π-Plot
Summary
There is the work by Ray and Lindsay ([6]) on the key features of multivariate normal mixtures, including the determination of the number of modes and general modality theorems. The literature on determination of the number of modes in logistic mixture models has focused primarily on univariate mixtures. Unlike the mixture of multivariate normal distributions (see [6]), for the logistic case it seems infeasible to express the ridgeline function explicitly. We focus on displaying the elevation of the logistic mixture density on the ridgeline and address a technique called the Π-plot, both of which carry important information about modality properties of the mixture. We conclude with remarks about the similarities and differences between the multivariate normal and logistic distributions in regards to their mixture properties and conclusions thereof
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