A delineation of new classes of exponential dispersion models supported on the set of nonnegative integers

Shaul K. Bar-Lev (), Gérard Letac () and Ad Ridder ()
Additional contact information
Shaul K. Bar-Lev: Holon Institute of Technology
Gérard Letac: Université Paul Sabatier
Ad Ridder: Vrije University

Annals of the Institute of Statistical Mathematics, 2024, vol. 76, issue 4, No 5, 679-709

Abstract: Abstract The aim of this paper is to delineate a set of new classes of natural exponential families and their associated exponential dispersion models whose probability distributions are supported on the set of nonnegative integers with positive mass on 0 and 1. The new classes are obtained by considering a specific form of their variance functions. We show that the distributions of all these classes are supported on nonnegative integers, that they are infinitely divisible, and that they are skewed to the right, leptokurtic, over-dispersed, and zero-inflated (relative to the Poisson class). Accordingly, these new classes significantly enrich the set of probability models for modeling zero-inflated and over-dispersed count data. Furthermore, we elaborate on numerical techniques how to compute the distributions of our classes, and apply these to an actual data experiment.

Keywords: Discrete distribution; Exponential dispersion model; Infinitely divisible; Lagrange inversion formula; Natural exponential family; Numerical computations; Variance function (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-024-00903-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-024-00903-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-024-00903-y

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().