New discrete heavy tailed distributions as models for insurance data

Saralees Nadarajah and Jiahang Lyu

PLOS ONE, 2023, vol. 18, issue 5, 1-34

Abstract: Although many data sets are discrete and heavy tailed (for example, number of claims and claim amounts if recorded as rounded values), not many discrete heavy tailed distributions are available in the literature. In this paper, we discuss thirteen known discrete heavy tailed distributions, propose nine new discrete heavy tailed distributions and give expressions for their probability mass functions, cumulative distribution functions, hazard rate functions, reversed hazard rate functions, means, variances, moment generating functions, entropies and quantile functions. Tail behaviour and a measure of asymmetry are used to compare the known and new discrete heavy tailed distributions. The better fits of the discrete heavy tailed distributions over their continuous counterparts as assessed by probability plots are illustrated using three data sets. Finally, a simulated study is performed to assess the finite sample performance of the maximum likelihood estimators used in the data application section.

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0285183 (text/html)
https://journals.plos.org/plosone/article/file?id= ... 85183&type=printable (application/pdf)

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:plo:pone00:0285183

DOI: 10.1371/journal.pone.0285183

Access Statistics for this article

More articles in PLOS ONE from Public Library of Science
Bibliographic data for series maintained by plosone ().