The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk

Shaul K. Bar-Lev, Ad Ridder

Research output: Contribution to journalArticlepeer-review


The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the right. Therefore, these distributions are well suited to fit count data with these properties. Furthermore, recent studies in actuarial sciences argue for the consideration of such distributions in the computation of risk factors. In this paper, we provide a thorough analysis of the LAEDM by deriving (a) the mean value parameterization of the LAEDM; (b) exact expressions for its probability mass function at (Formula presented.) ; (c) a simple bound for these probabilities that is sharp for large n; (d) a simulation algorithm for sampling from LAEDM. We have implemented the LAEDM for statistical modeling of various real count data sets. We assess its fitting performance by comparing it with the performances of traditional counting models. We use a simulation algorithm for computing tail probabilities of the aggregated claim size in an insurance risk model.

Original languageEnglish
Article number3715
Issue number19
StatePublished - Oct 2022
Externally publishedYes

Bibliographical note

Funding Information:
This research was partially funded by STAR (Stochastics—Theoretical and Applied Research) and NWO (Netherlands Organization for Scientific Research) grant number 040.11.711.

Publisher Copyright:
© 2022 by the authors.


  • count data
  • exponential dispersion model
  • Monte Carlo simulation
  • natural exponential family
  • variance function

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Mathematics (all)
  • Engineering (miscellaneous)


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