A New Generalized t Distribution Based on a Distribution Construction Method

Ruijie Guan, Xu Zhao, Weihu Cheng and Yaohua Rong
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Ruijie Guan: Faculty of Science, Beijing University of Technology, Beijing 100124, China
Xu Zhao: Faculty of Science, Beijing University of Technology, Beijing 100124, China
Weihu Cheng: Faculty of Science, Beijing University of Technology, Beijing 100124, China
Yaohua Rong: Faculty of Science, Beijing University of Technology, Beijing 100124, China

Mathematics, 2021, vol. 9, issue 19, 1-36

Abstract: In this paper, a new generalized t (new Gt) distribution based on a distribution construction approach is proposed and proved to be suitable for fitting both the data with high kurtosis and heavy tail. The main innovation of this article consists of four parts. First of all, the main characteristics and properties of this new distribution are outined. Secondly, we derive the explicit expression for the moments of order statistics as well as its corresponding variance–covariance matrix. Thirdly, we focus on the parameter estimation of this new Gt distribution and introduce several estimation methods, such as a modified method of moments (MMOM), a maximum likelihood estimation (MLE) using the EM algorithm, a novel iterative algorithm to acquire MLE, and improved probability weighted moments (IPWM). Through simulation studies, it can be concluded that the IPWM estimation performs better than the MLE using the EM algorithm and the MMOM in general. The newly-proposed iterative algorithm has better performance than the EM algorithm when the sample kurtosis is greater than 2.7. For four parameters of the new Gt distribution, a profile maximum likelihood approach using the EM algorithm is developed to deal with the estimation problem and obtain acceptable.

Keywords: generalized t distribution; order statistics; EM algorithm; improved PWM; parameter estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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