The modality of skew t-distribution

The aims of this paper are to study the modality of skew t-distribution and the mixture of skew t-distributions graphically and analytically. We introduced a new formula to find the modes for univariate skew t-distribution and the mixture of univariate skew t-distribution. We also explored the effect of the skewness parameters and the degrees of freedom on the number and locations of modes for univariate skew t-distribution and in the mixture of skew t-distribution. Exploring the modes for the mixture of skew t-distribution helps the research to discover when and which components of the mixture can be merged in one homogeneous group to get the best results when exploring the data set.

Automated summary

This paper studies the modality of skew t-distribution and the mixture of skew t-distributions graphically and analytically. A new formula is introduced to find the modes for these distributions. The effects of skewness parameters and degrees of freedom on the number and locations of modes are explored, as well as the merging strategy for components in the mixture model.