Measuring Discrete Risks on Infinite Domains: Theoretical Foundations, Conditional Five Number Summaries, and Data Analyses

Daoping Yu, Vytaras Brazauskas and Ričardas Zitikis

North American Actuarial Journal, 2024, vol. 28, issue 3, 678-694

Abstract: To accommodate numerous practical scenarios, in this article we extend statistical inference for smoothed quantile estimators from finite domains to infinite domains. We accomplish the task with the help of a newly designed truncation methodology for discrete loss distributions with infinite domains. A simulation study illustrates the methodology in the case of several distributions, such as Poisson, negative binomial, and their zero-inflated versions, which are commonly used in the insurance industry to model claim frequencies. Additionally, we propose a very flexible bootstrap-based approach for use in practice. Using automobile accident data and their modifications, we compute what we have termed the conditional five number summary (C5NS) for the tail risk and construct confidence intervals for each of the five quantiles making up C5NS and then calculate the tail probabilities. The results show that the smoothed quantile approach classifies the tail riskiness of portfolios not only more accurately but also produces lower coefficients of variation in the estimation of tail probabilities than those obtained using the linear interpolation approach.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10920277.2023.2285976 (text/html)
Access to full text is restricted to subscribers.

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:taf:uaajxx:v:28:y:2024:i:3:p:678-694

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/uaaj20

DOI: 10.1080/10920277.2023.2285976

Access Statistics for this article

North American Actuarial Journal is currently edited by Kathryn Baker

More articles in North American Actuarial Journal from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().