On a Novel Skewed Generalized t Distribution: Properties, Estimations and its Applications (2401.14122v1)

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 paper, 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.