On a novel skewed generalized t distribution: Properties, estimations, and its applications

Abstract

With the progress of information technology, large amounts of asymmetric, leptokurtic, and heavy-tailed data are arising in various fields, such as finance, engineering, genetics, and medicine. It is very challenging to model those kinds of data, especially for extremely skewed data, accompanied by very high kurtosis or heavy tails. In this article, we propose a class of novel skewed generalized t distribution (SkeGTD) as a scale mixture of skewed generalized normal. The proposed SkeGTD has excellent adaptiveness to various data, because of its capability of allowing for a large range of skewness and kurtosis and its compatibility of the separated location, scale, skewness, and shape parameters. We investigate some important properties of this family of distributions. The maximum likelihood estimation, L-moments estimation, and two-step estimation for the SkeGTD are explored. To illustrate the usefulness of the proposed methodology, we present simulation studies and analyze two real datasets.

Keywords:

• Skewed generalized t distribution
• maximum likelihood estimation
• L-moments estimation
• two-step estimation
• EM algorithm

Acknowledgments

The authors wish to express their deepest gratitude to the chief editor, the associate editor, and two referees whose careful reading and comments led to an improved version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was supported by the National Natural Science Foundation of China (No. 11701021), National Statistical Science Research Project (No. 2022LZ22), and Science and Technology Program of Beijing Education Commission (No. KM202110005013).