Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution

Shaul K. Bar-Lev, Xu Liu (), Ad Ridder and Ziyu Xiang
Additional contact information
Shaul K. Bar-Lev: Faculty of Industrial Engineering and Technology Management, Holon Institute of Technology, Holon 5810201, Israel
Xu Liu: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
Ad Ridder: School of Business and Economics, Vrije University of Amsterdam, 1081 HV Amsterdam, The Netherlands
Ziyu Xiang: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China

Mathematics, 2024, vol. 12, issue 13, 1-21

Abstract: The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has not been used for statistical aspects. Out of all EDMs belonging to the Tweedie scale, only two EDMs are steep and supported on the whole real line: the normal EDM with constant variance function and the EDM-EVF. All other absolutely continuous steep EDMs in the Tweedie scale are supported on the positive real line. This paper aims to accomplish an overall picture of all generalized linear model (GLM) applications belonging to the Tweedie scale by including the EDM-EVF. This paper introduces all GLM ingredients needed for its analysis, including the respective link function and total and scaled deviance. We study its analysis of deviance, derive the asymptotic properties of the maximum likelihood estimation (MLE) of the covariate parameters, and obtain the asymptotic distribution of deviance, using saddlepoint approximation. We provide numerical studies, which include estimation algorithm, simulation studies, and applications to three real datasets, and demonstrate that GLM using the EDM-EVF performs better than the linear model based on the normal EDM. An R package accompanies all of these.

Keywords: exponential dispersion model; generalized linear model; exponential variance function; small-dispersion asymptotics; saddlepoint approximation; analysis of the deviance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/13/2021/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/13/2021/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:13:p:2021-:d:1425352

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().